newest version (13.5.6) has a password (fullivs) so all your pkmn have perfect ivs. shiny mons will not have perfect ivs unless you also breed for those or use the password or use cell imprints to max each iv individually (gotten from certain zygarde cell thresholds and from mr. luck for some black prisms)
unsure about the other question
the wiki.gg is a work in progress but already has the newest aevian forms, you're likely on the (abandoned) fandom wiki. after you get fly (the HM, not the badge for it, so late chapter 13), the move relearner is able to teach egg moves
then you're missing one of the previous battles
check the previous places one by one, ive seen at least 2 saves where the quest progression got reset for some reason
hhmm im talking to someone else and they asked if you are sure you completely finished hidden library 3
the end is karen staying in the unown dimension and you and karrina coming back, then later when the twins appear in gdc, karen is with them. did that happen in your save?
1. there are more than 3 quests in the help center, both abnormal and secrets are available in there. make sure you talked to the board
2. the kristiline help center keys are only available after you finish all kakori quests
there are 5 kakori quests initially