Six years on, I can contribute further to this question by presenting solutions for all three 'messages' (only one was found up until now). However, using that information to deduce quite who or what Godot is still eludes me, though I do have one suggestion that may be worth a shout (in bold text in last spoiler block). Perhaps someone else can finally close this one off?
Message 2:
As @GarethMcCaughan discovered in August 2016:
The second message is actually a partially completed 7x7 word square, with rows and columns reflected (reflection clued by a reference to 'just the opposite'). I reproduce it here (reflected back to a readable state):
B R I[S]T L E
R E N E W A L
I N C L I N E
[S]E L F D O M
T W I D D L E
L A N O L I N
E L E M E N T
The 'S' is the letter represented in the original message by an '!' icon. And as Gareth surmised, the word 'SELFDOM' (which was entirely absent in the original message) is clued by the quote "You're as bad as myself."
We can use similar thinking to solve the other two messages...
Message 1:
This message can be solved by noting that:
Each ROW is an anagram of a word required to make a 7x7 word square. Moreover, the three quotes beneath the grid provide clues/confirmation for the identities of the three totally absent words - TOBACCO (smoker), CALLANT (boy) and OLDSTER (white hair and general gist).
[T]O B A C C O
O V E R A L L
B E V E L E D
A R E O L A S
C A L L A N[T]
C L E A N S E
O L D S[T]E R
The '$' icon represents three instances of the letter 'T'.
Message 3:
This message can be solved by noting that:
Each COLUMN is an anagram of a word required to make a 7x7 word square. In the absence of any totally missing words, the significance of the quote underneath is less immediately obvious. It might possibly be to help differentiate the ambiguities in the two icon-marked spaces: '*' could be C, H or L to form _ASSOCK, while '?' could be I or R to form SER_ATE, but 'Vladimir sways back and forth, doubled in two' might suggest an image of somebody praying on a HASSOCK and 'doubled in two' might suggest 'SERIATE'. Possibly though it suggests something else entirely...
[H]A S S O C K
A Z T E C A N
S T Y R E N E
S E R[I]A T E
O C E A N I C
C A N T I N A
K N E E C A P
As for finding Godot himself...
...what do we do next?
If, as Gareth surmised, we are to anagram the four character-concealed letters, among other possibilities Godot might be HIST(ory) or a SITH, or we may be learning that "IT'S H!" (Though I somehow doubt that Godot is a member of the TSHI people of Ghana...) Using the alternatives from grid 3 yield nothing more obviously correct - except that just maybe, THIS is Godot; as in these missing letters within this puzzle, missing exactly as our mysterious Godot has been all along, meaning that by finding these letters we have actually found 'Godot' and no more 'waiting' need be done! It's a thought...
I had also considered that perhaps the second word square might need to be presented in its reflected form (as originally), but can spot no real utility of doing this. Overlaying grids and looking for commonalities yields very few (seemingly none of use), and I'm struggling to spot any benefit of using three T's and two S's as per the total number of hidden characters in their grids.
Putting this all here in an answer to see if it inspires anybody else to (re)visit this one and see it through to the end at long last...