I think, whether those notes are genuine or not, that the boys are going to be in a kind of news blackout zone in the cave. The rescuers have to keep their spirits up and keep their fears to a minimum and allay as much sense of panic as they possibly can.
In that situation those notes do seem plausible that the kids might worry about homework and want to reassure their families that they are okay? The mentions of food seem consistent with people who've been starved for ten days and then on MREs and liquid nourishment to replenish their system, not anything like proper food.
IMHO, if the notes are fakes, they've been extremely well compiled from a psychological standpoint?
ETA the note from the coach has a terrible sense of guilt in it? Could someone fake that in order to have positive-sounding words but a thread of guilt running through them?
ETA 2....maybe there's some partial doctoring...for instance if a boy writes "I'm scared" that gets changed to "I'm okay"?
It's hard to tell, but if the whole things are faked, I think it's an extremely high-quality job that few people would be capable of? But the translation into English is also surprisingly excellent and flowing English, it doesn't sound like the sort of thing from an automatic translator. It would be interesting to be able to read it in the original language (for a native Thai speaker).