Don't schools have special ed rooms to help dyslexics learn?
Unfortunately, the matter isn't as simple as that. You see, there have been times and still are times where the education system has failed and, as sad as it is, some kids have been "pushed along", which is to say, just sent to the next grade or given passing grades without any sort of help. Naturally, Annie is supposed to serve as a metaphor for such.
You also have to take into account that as she said, Annie has been really good at hiding her illiteracy. For example, she gives a highly creative and engaging history report off the top of her head. It could be that she does well enough in other areas for teachers not to notice much. Additionally, even if someone did notice, Annie could've fibbed her way out of the confrontation. If the adult went to Ms. Hannigan about it, such as requesting a parent-teacher conference...well, it's not like she'd care.
Nearly every child in America goes to school and yet adult illiteracy is A Thing, so clearly it's entirely possible for this to happen. Dyslexia, one possible explanation for Annie's problems with reading, is frequently not even diagnosed until adulthood. The thing is, dyslexics tend to be both strategic and lateral thinkers, finding ways around difficulties like this either consciously or unconsciously. Not all parents or even teachers understand how various Special Educational Needs manifest and miss the signs. And that's in people with nurturing and stable upbringings. In the film, Annie's illiteracy is a sign that although on the surface the girl's childhood is not the obvious Orphan's Ordeal of the original, the lack of adult care and attention has really had a tangible affect. Schools do have Special Educational Needs programs but often it's the parents/guardians who have to alert the school to the problems their child is having. If Miss. Hannigan - or any other foster parent - had sat down to help her with homework even once, Annie's issues would have become apparent. And as for teachers picking up on it, Annie has probably moved school at least once, is a bit of a cheeky troublemaker, making it easy for teachers to mistake her bad or missing work for shirking, and she's clearly very bright. In short, there is really no headscratcher here, just a sadly too-common story of someone getting lost in the system and adults dropping the ball.
If Annie never learned to read, then how did she know what the note from her parents said?
Presumably someone read it to her, and then she memorized it.
Forget being in school or the note from her parents - if Annie can't read, how the hell did she fill out all those forms when she was looking for information on her folks?
She didn't. One of the girls copies the information needed on the form for her while Annie distracts Miss Hannigan.
The fake parents tell Annie that "Stacks doesn't need you anymore. Why do you think we're taking you?" Why do the fake parents think Stacks paid them and not Guy?
Because Guy's goal is to make Stacks win the election. It's not much of a surprise that they'd assume Stacks is behind it and left all dirty negotiations with Guy in order to have some sort of plausible deniability. There's also the possibility they don't really think Stacks paid them off and were just being needlessly cruel to Annie.
Why did Mr. Stacks not tell Annie as soon as she was rescued that Guy was behind the entire scheme?