Partial
starthere.txt: Your father has gone missing. You, two brothers , are off to an adventure to find him. The only thing that he left you is a 4x4 crossword with following clues:
0) A su[pe]rficial excuse for discrimination (4) -> skin (from pirate)
1) When I .... about politics you always seem to .... (4/4) -> talk/yawn (from pirate)
2) Italy relative to Croatia (2) -> sw (southwest)
2) Way to get loved for quite some time, time, time (4) -> stay (according to Taylor Swift)
3) A letter, best fitting Poseidon (3) -> psi, which looks like a trident
3) Vatican relative to Italy (2) -> in
The crossword seems to be the one in the centre of the image. Insert the letters and solve the grid as a slitherlink (this was figured out by Omega Krypton):
You decide to take everything from the house to help you on your quest. Take everything within the walls, or out the walls of the house, depending on the brother you play for (7/7). After that, to get your number even, you drink some tea (+1/+1) and embark on your separate journeys.
The outside letters (SKYPAWN), with an additional T, fit to gryphon.txt, which we'll get to once we need to. The inside letters (STAALSI), with an extra T, fit to oceanman.txt. Let's solve that one as far as we can first.
oceanman.txt: You decide to TRAVEL on board of a ship, called after some HOLY person. Suddenly, you get into the storm, and the ship gets wrecked!!! Having drunk lots of SEAWATER, you get onto the seashore alive.
We have STAALSIT, so travel = SAIL, holy = ST, seawater = SALT. Which fits in the middle left.
You're barely alive. Leave only one from each set of same letters you have (-3).
This leaves ALSIT.
robocop.txt: Roaming across the land, you bump into a big smart COMPUTER. He looks at you, and decides to help you if you find him SEVERAL items.
This is computer = AI, several items = LIST. These fit in the bottom-most crossword.
Though you helped him a lot, the computer can give you only a bucket of completely non-edible metal items. Add all missing letters to the pile (+1).
Non-edible metal items are NAILS (thanks GentlePurpleRain). We get one extra N here, giving ALSITN.
redalert.txt: You meet a furious leader with a MOUSTACHE. He wants you to advice him on how to rule the country.
The moustached leader is STALIN. This fits the crossword in the bottom right corner.
Seeing the politics from the inside has straightened your mind. Iterate each letter from the pile through the alphabet, until it gains a vertical symmetry. (+0)
S -> T, L-> M, N -> O, giving TTAMIO. (from Ben J)
einstein.txt: You go to COLLEGE (to get some knowledge, of course). There you move on to conducting experiments with NUCLEAR powers.
College = MIT, nuclear = ATOM (from Ben J). The crossword is near the bottom left corner.
Your experiments are a success! Take every pair of same letters you have, then turn them into 4 adjucent letters (say CC turns into ABDE). Being incredibly smart now, you head into an expedition! (+2)
TTAMIO -> RSUVAMIO
edge.txt: Reaching the very EDGE of the world, you suddenly feel a strange TASTE on your tongue. It appears that you're a psychic and your brother requires your help right now! No time for research now!!!
Edge = RIM, taste = SAVOUR. This fits the topmost crossword.
Exchange your letters for what is bothering your brother (-8+4). After that add brother to the pile (+7). Seems like that saved him, and your adventure continues.
Appears we now need to go back to the Gryphon part to figure out what we need...
gryphon.txt: After spending a continuous time in the SUNNY south, you look UP and see a terrible beast flying into you. However, you manage to cut its LEGS, and it falls to the ground.
We have the letters SKYPAWNT from starthere.txt. So up = SKY, legs = PAWS, sunny = TAN. Which fits in the bottom left crossword.
You end the creature's life. You take its undamaged parts as a trophy - add all missing letters to your pile (+2).
Since we cut off the gryphon's legs, the undamaged part is WINGS, which would give us two new letters leaving SKYPAWNTIG.
kingsman.txt: You turn to serve a great LEADER, who tends to wear BRIGHT royal clothing. He puts your MIND to a good use and sends you to GATHER information on the neighbouring country's army.
Leader = KING, bright = GAY, mind = WITS, gather info = SPY. This fits the leftmost crossword.
The king sees you want to drink something, but your crossword is missing a letter of it. Being kind, he grants you this exact letter thrice (+3).
The crossword has T_A with a hole in the middle, so it's missing an E for "tea" (from OP). So we get SKYPAWNTIGEEE.
cake.txt: You meet a pirate, who desires to bake a cake. His problem being, his evil BROTHER locked the recipe BOOK inside a tresure chest! After you pick the LOCK, you see that the pirate misses one INGREDIENT from the cake.
brother = TWIN, book = PAGE, lock = KEY, ingredient = YEAST (from Omega Krypton)
You acquire the missing ingredient, and, though the resulting cake tastes like garbage, the pirate shares one of his secret treasures with you (+1).
"X" marks the spot, so we get an extra X. We have SKYPAWNTIGEEEX now.
dream.txt: You meet a BEAUTIFUL girl, who appears to be a videogame NERD as well. The COLOUR of her skin, the size of her HIPS - everything is just as you could ever wish for.
beautiful = SEXY, nerd = GEEK, colour = PINK, hips = WAIST. This fits the crossword at the bottom middle.
You fall madly in love and marry her. Lot of things you were attached to before now seem unneeded: remove three letters from the left, one from the right and one from below (-5).
The three leftmost letters are WEG, the rightmost one is T, and the bottom-most one is Y. We're left with PAISNEEKX.
ambush.txt: You decide to perform a heist. As you sneak into the TOWER, you are ambushed by SEVERAL guards! They HURT you very much and throw into the streets to die.
Tower = KEEP, several = SIX, hurt = PAIN. This fits a crossword near the bottom right corner.
As you're almost dead, you feel angelic help removing what was bothering you (-4). Instead of that you get letters of unknown origin (+8). Now you're once again healthy and alive.
Remove PAIN, and from edge.txt above, we know the letters we receive are RSUVAMIO. We're left with SEEKXRSUVAMIO.
bigcitylife.txt: You BLEND into the crowd and try to start a new life. You wear a DISGUISE as a street poet. However, after your every POEM peope around just get GLOOMY.
Blend = MIX, disguise = MASK, poem = VERSE, gloomy = SOUR. These fit near the top right corner.
You grow a longish beard and reconsider life: for every letter that has an empty space below, add a previous aphabetically letter to that space (+7). Maybe, you should get back to your wife.
The letters with nothing below them are VERKEIX. So we add UDQJDHW, leaving us with SEEKXRSUVAMIOUDQJDHW.
family.txt: Suddenly, you are a father of three nicest CHILDREN! That's like a small ARMY! One of them wants to cut LUMBER, the other wants to join american TROOPS, the third, however, considers himself a COMMUNIST. However you think this is a FAD he picked somewhere. However, this kid is the only one that reacts to your every PUN, so you like him most.
Children = KIDS, army = SQUAD, cut lumber = AXE, American troops = USV (United States Volunteers), communist = RED, fad = WHIM, pun = JOKE. These fit the big one at the top middle.
Your life is cozy and well-regulated. However, it's hard to remember things with all that racket around. Leave only the biggest rectangle of letters within your crossword (-10).
Remaining letters are OKHIADXSED.
...The remaining have no place in the story so far but have some preliminary solutions...
myback.txt: Your SPINE suddenly hurts so much, you feel as a living CORPSE. You feel an incredible urge to visit a place, as though you've been CURSED. After saying that everything's ALLRIGHT to your wife, you go for a walk.
I think the solution is BACK, BODY, POX and OK, which fits a crossword on the middle right. Letters: POXBACKODY
You come to your destination feeling a bit better. Leave only the biggest symmetrical shape of your crossword (-2).
Removing P and O makes the crossword symmetrical. So we're left with XKCDOBAY.
Too bad that there are no crosswords left which take 8 letters...
airdanger.txt: You're attacked by a dreadful BEAST! It SHOUTS at you something about avenging his brother. However, you don't want to hurt this monster. You tell him about how you SYMPATHISE his feelings, while you sneakily throw a calming MEDICINE into him. The beast is touched by your words. You persuade him to have a fresh start and send him to help your old FRIEND.
Not sure where in the story this fits, but the solution has to have letter counts of (2,4,4,4,7) since there's only one place left with five words (top left). Given gryphon.txt, this could be beast = GRYPHON, shouts = ROAR, sympathise = PITY, medicine = CURE, but that would leave a two-letter word for "friend" which ends in I...?
Your friend says thanks for a new winged helper. Add the first half of the word to the pile (+1).
A two-letter word for thank you is "ta". So we'd add T to leave TPITGRYPHONRARCUE? (last letter unknown)...
roaringbeauty.txt: You come upon a definitely suffering BEAST in the forest. Having a closer look, you see that it's struggling to get out of woman's CLOTHING. After you decide to help it, out of the kindness of your pure heart, you see the beast turn into a princess. She tells you her sad STORY, and you fall in love at the first sight (given she's still naked).
This could be BOA, BRA, FANTASY, which would fit directly next to the central square. Then again, maybe there are other options...
You want to know her a bit better. Add the not-so-necessary letters to one of the words (+6).