Original answer introduction by Jeremy Dover: This puzzle is pretty epic! I've got four of the components solved, but need to stop for the night, so I figured I'd write them up as a community Wiki so others can contribute. Feel free to add to this answer, or post your own if you crush the whole thing!
13 - Jeremy Dover
Who's been erased from history?
Looking at the grid, you notice there are a lot of names, particularly at the bottom: RICHARD, GEORGE, ELIZABETH, EDWARD...these are all monarchs of Great Britain! Treating the grid as a word search, it turns out there are two ELIZABETHs, six GEORGEs, eight EDWARDs...as there should be, since there have been two ELIZABETHs, etc. Heck, I never even knew there was a King STEPHEN. But who's missing? Well, there are only three WILLIAMs in the grid, but there were four Kings named WILLIAM, most recently the uncle and predecessor of Queen Victoria.
The completed grid:
As one might expect, there is an Easter Egg in here...the covered letters roughly form the shape of a crown. There's also a LONDON uncovered in the upper right...might be coincidence, but just to point it out. Note also that the question is "Who's been erased from history?" suggesting the question might be a clue to the puzzle.
Note from OP:
There was a second Easter Egg concealed within this puzzle, intended as an additional hint - if you look at the unused letters within the crown shape, reading these from top-to-bottom and left-to-right spells 'EIGHTEEN THIRTY' - the year which the missing king, William IV, ascended to the throne.
Also, if we are being absolutely correct, the names hidden in this grid are technically those of all of the officially recognised kings and queens of England/GB/UK (not merely Great Britain, which was not a political union until 1707) since William I came a-conquering in 1066. Conveniently, this produced a list of 13 different names, which is what I required for this sub-puzzle!
12 - Jeremy Dover
Who has left the table?
In this puzzle, notice that the question is "Who has left the table?". Table? And a lot of numbers less than 119? And Stiv? Gotta be the Periodic Table! If you replace each number with its associated atomic symbol, you get a set of one or two character glyphs, which can be anagrammed into names. Notice that the first letters are never given, and that the question marks refer to letters that cannot be encoded using the periodic table.
The easiest ones to get are the first, where "ND" "W" and "RE" seem to have to anagram as ANDREW, the third which is clearly JAMES, and "O", "H" and "N", which will give JOHN. These are the apostles of Jesus Christ. Once you have this, the rest fall into place. The complete grid:
Note from OP:
I took particular pleasure over the sub-title used for this sub-puzzle, as it actually has a double meaning - not only might the use of 'table' conjure up the idea of the Periodic Table, but it also carries an allusion to Leonardo da Vinci's painting, The Last Supper, at which Jesus and his disciples sit to eat along a long table:
11 - M Oehm
Who's gone off the map?
The first names of the shown people refer to countries or national capitals named after a saint, possibly in another language:
Dominic Monaghan — Santo Domingo, Dominican Rep.
George Clooney — St. George, Grenada
(not shown) — Basseterre, St. Kitts and Nevis
Lucy Liu — Santa Lucia
Marinus "Rinus" Michels — San Marino
Thomas Alva Edison — São Tomé, São Tomé and Príncipe
Vincent van Gogh — Kingstown, Saint Vincent and the Grenadines
James Brown — Santiago, Chile
John McEnroe — St John, Antigua and Barbuda
Joseph Heller — San José, Costa Rica
Salvador Dalí — San Salvador, El Salvador
These capitals are all in the regions marked on the map and the colour seems to refer to how many are found in each region.
The people are arranged in a cross, a hint towards Christian saints. The names in the stem of the cross are national capitals named after a saint. The names in the crossbar are countries named after a saint. (San Marino and São Tomé in the, erm, cross section have the same name for country and capital.) Within their category, the names are arranged alphabetically.
We need a country named for a saint: St. Kitts is another name for Christopher.
10 - Jeremy Dover
Who's lost in the supermarket?
In this puzzle, the first key is to identify all of the people and produce. Some knowledge, and some TinEye yield the following identifications:
Produce: BEAns, ARTichoke, LEEk, ALFalfa, MELon, CHErry, PEPper, TANgelo, TOMato, ORAnge
People: ALF ramsey, MEL gibson, BEA arthur, rita ORA, bruce LEE, TAN france, ART garfunkel, PEP guardiola, CHE guevara
Notice that each of the people has either a first or last name with only three letters, and those three letters form the first three letters of one of the produce items: ALF ramsey <=> ALFalfa, etc. The odd produce out is the TOMato, showing that our missing person must be named 'TOM'.
9 - Jeremy Dover
Who's been cast out from the family?
This is a 'cryptic family reunion', so the family member name in each cryptic clue is a stand-in for the answer. I have to admit I kinda cheated on this one, based on the shape in which the clues are placed, and the fact that I picked out the upper right answer GREG pretty quickly. The answers to the clues are the first names of the members of The Brady Bunch, from the 1960s US sitcom. I literally watched this show every day from age 7 to age 12. Even the crappy episodes with Oliver. The shape in which they are placed corresponds to the introduction to the show, which shows the nine characters in a 3x3 grid which corresponds exactly to the answer. So I already knew the answer was PETER. Note also that the family members chosen correspond exactly to the relationships within the show, relative to the missing member.
'Sister from another mister' corresponds with security service after breaking arm
MARCIA = CIA [security service] after ARM*
Monster turns up outside Cinderella's basement - end of evil stepmother
CAROL = ORC< [monster] outside _A + _L
Older brother red-faced, covered in scrambled egg
GREG = R_ cover in EGG*
Father's stepdaughter is indeed in Germany (near Berlin Wall)
JAN = JA [indeed in Germany] + _N [Berlin "wall"]
Champion boxer takes tips from concierge, becomes housekeeper
ALICE = ALI [champion boxer] + C_E [tips from concierge]
Young baseball player eats hot dog starter for stepsibling
CINDY = CY [Cy Young] eats IN [hot] + D_ [dog starter]
Father held up by Hideki Matsuyama
MIKE = hidEKI Matsuyama<
Little bro has short haircut and bony cheeks
BOBBY = BOB [short haircut] + B_Y [bony cheeks]
Note from the OP:
I must admit I wasn't at all disappointed and in fact found it highly satisfying that Jeremy managed to 'cheat' (in his words) and take the shortcut to the answer here! As Jeremy points out above, the cryptic clues here were arranged in the exact layout used in the show credits:
Not only that, but the shade of blue I used for the background of the image was eyedropped straight from a still.
Finally, I enjoyed the use of 'cast' in 'cast out' within this sub-puzzle's sub-title, with its alternative meaning relating to a group of actors...
8 - M Oehm
Who's gone quiet?
The "equalizer LEDs" are names written in Braille, with empty spaces without dots removed, set flush left and rotated by an anticlockwise quarter-turn.
To illustrate: Write the first name, ALEC, in Braille, using a different colour of the rainbow for each letter. Then turn everything to the left, so that the dots "fall" to the floor, making nice, Tetris-like stacks:
R · O · Y · G G R O Y G G
· · O · · Y · · O Y
· · O · · · · · O
That gives us Alec, Hugh, Tico, Dave, Phil, Richie and David. The masked words to the right are roles in a band, namely bAss, drUms, gUItAr, kEybOArd and vOcAls. We're looking for a guitarist and vocalist in a band where the others are or have been members. That's Jon Bon Jovi.
7 - user39583, augmented by Darrel Hoffman
Who's the one that got away?
We can reorder the letters to form clues:
NUMBER OF NAPIER OR EULER = e
ROOT OF MINUS ONE = i
FIFTY FOR ROMANS = l
SHEFFIELD POSTCODE AREA = s
TESLA TIME OR TON = t
VANADIUM SYMBOL = v
UPRIGHT AXIS TAG = y
RUSSIAN YES WORD = da
BUDDY OF EGO AND SUPER-EGO = id
PYTHON KNIGHT UTTERANCE = ni
SAUDI WEB DOMAIN = sa
EAST-NORTHEAST FOR SHORT = ene
FEYENOORD LEROY = fer
CHOP OR HACK DOWN = hew
UK JELLY = jam
IT CROWD MANAGER = jen
FRONT DOORSTEP WELCOMER = mat
BADMINTON PITCH = court
In fact, if we take the dot colours after each of the strings, the colours are always reordered RBYRYB with one of the colours replaced by white and the string with no dot coming last. The white dot's position in the order tells us which answers belong together and gives the following names:
1. (wbyryb) JENNIFER (Aniston)
2. (rwyryb) COURTENEY (Cox)
3. (rbwryb) LISA (Kudrow)
4. (rbywyb) MATTHEW (Perry)
5. (rbyrwb) DAVID (Schwimmer)
6. (rbyryw) JAMES (Michael Taylor)
These are actors from Friends with appearances in over 100 episodes, missing only Matt LeBlanc.
Note that the order of the dot colors isn't arbitrary - they follow the order of the dots that appear between the letters in the actual logo for the show (which also corresponds to the umbrellas they use in the intro). The letter font is also a (loose) attempt to draw a resemblance to that logo:
6 - Jeremy Dover
Who's been scared off?
The pictographs in the book represent the characters in Harry Potter and the Chamber of Secrets who (SPOILER ALERT!) are petrified by the basilisk, and the means through which they avoided actual death (i.e. avoided looking directly into the basilisk's eyes). In order:
* Mrs. Norris (Argus Filch's cat) merely saw the basilisk's reflection in a puddle.
* COLIN Creevey saw the basilisk through a camera.
* Justin Finch-Fletchley saw the basilisk through the ghost of Nearly Headless Nick.
* Nearly Headless Nick was already dead, so he could not be killed.
* Penelope Clearwater and Hermione Granger saw the reflection of the basilisk in a hand mirror.
5 - oAlt, augmented by Darrel Hoffman
Who's lost for words?
Upon closer inspection, four names seem to be hidden as substrings within each sentence, and each name seems to belong to one of the most recent Prime Ministers of the United Kingdom:
PuT ON Your...
..talkinG - OR DON't you...
THERE'S A fist here...
...puB OR I Shall drag...
In fact, these are the five most recent UK prime ministers, with one skipped (Tony Blair, Gordon Brown, ..., Theresa May, Boris Johnson). The fact that there's a fifth person, in the middle of the image, confirms that we indeed need to identify that skipped person. So "the one who's lost for words" is most likely the missing Prime Minister in this list, David Cameron.
(Note also that we know we have to be looking for UK Prime Ministers, as the color of each person corresponds to the color associated with the political party to which their concealed Prime Minister belongs. e.g. Boris Johnson is of the Conservative party, which is represented by the color blue, and one of the blue people spoke the sentence with "Boris" hidden in it. The choice of the man or woman icon also represents the gender of each person.)
4 - M Oehm
Who's not being listened to?
The three song titles are anagrams of three songs by The Beatles: I am the Walrus written by John Lennon, While my Guitar Gently Weeps written by George Harrison and Octopus's Garden written by Ringo Starr. That leaves Paul McCartney as the Beatle without a song represented in this image, and who thus 'isn't being listened to'.
3 - Masclins & phyatt
Who's all at sea?
Who lives in a pineapple under the sea? SPONGEBOB SQUAREPANTS! The images correspond to the three houses belonging to the main characters in SpongeBob SquarePants:
Moreover, the selected colours and the enumerations given by strings of 'X's correspond to the skin tones and names of the characters who inhabit them:
Xxxxxxxxx = Squidward (9 letters, blue)
XxxxxxXxx = SpongeBob (6+3 letters, yellow)
??????? = Patrick (7 letters, colour not given)
2 - Jafe
Who's out of the picture?
a picture of Tweety in the poster of "I Tawt I Taw a Puddy Tat", with part of the film title showing. Sylvester the cat is missing from the picture.
Note from the OP:
This is the sub-puzzle that took the longest to construct, and yet it fell very quickly! I wanted to make sure that the nonogram was actually entirely solvable through deduction alone, with no guesswork at all, and without making an assumption of symmetry for the main image. I have no idea if Jafe took any shortcuts on the way to a solve (I honestly don't mind) but at least I could sleep at night knowing the nonogram's quality was intact :)
One further remark: I hadn't actually intended this as a direct representation of the movie poster, instead working off a cartoon still found online, and meant for the answer 'Sylvester' to be deduced merely as the missing feline member of the cartoon double act - the 'puddy tat' absent from Tweety Pie's catchphrase written below the image. The fact Jafe found this other image was a bonus!
1 - oAlt
All of the names that have occurred are the first names of actors who have played the lead role of The Doctor in the long-running BBC drama series Doctor Who:
13. WILLIAM Hartnell (The First Doctor)
12. PETER Davison (The Fifth Doctor)
11. CHRISTOPHER Eccleston (The Ninth Doctor)
10. TOM Baker (The Fourth Doctor)
9. PETER Capaldi (The Twelfth Doctor)
8. JON Pertwee (The Third Doctor)
7. MATT Smith (The Eleventh Doctor)
6. COLIN Baker (The Sixth Doctor)
5. DAVID Tennant (The Tenth Doctor)
4. PAUL McGann (The Eighth Doctor)
3. PATRICK Troughton (The Second Doctor)
2. SYLVESTER McCoy (The Seventh Doctor)
The only actor who has played the good Doctor (to date) and whose name has not yet been listed is the current incumbent, the Thirteenth Doctor, JODIE Whittaker!
A final note from the OP:
Thanks to all the solvers who contributed towards solving this puzzle - it was a joy to watch your minds at work! I hope now that the final answer has been found you can all appreciate the significance of the title of this puzzle...!