Question: When Dr. Strange separates Peter's spirit from his body how is Peter still able to make his arm move?
Answer: I guess I missed something because I thought that suit was made with Stark tech and has nanotech in it. I figured it was the suit keeping the box away and Doctor Strange thought it was Peter.
Question: Are the Tobey Maguire and Andrew Garfield Spider-Man movies now part of the MCU?
Answer: No, they are part of the multiverse. The MCU is just one of those universes within the multiverse.
Answer: I almost think the best way to refer to them would be to call them "MCU-Adjacent." Both answers nail it - they're not part of the MCU universe itself, but are canonical to it and co-exist alongside it thanks to the establishment of the multiverse. And considering the "Doctor Strange and the Multiverse of Madness" trailer teases Patrick Stewart as (presumably) Professor X, I think we could probably also apply this to pretty much any other Marvel adaptation ever made that was not made by Marvel Studios itself. It all co-exists and is all canonical to each other through the use of multiverses/alternate timelines/alternate dimensions.
Answer: No. It's explained that they are from another universe, and were sent back to their universes at the end of the film.
Question: Surely 'curing' the villains and sending them back to their own universes will have severe implications on the timeline. For example if Norman Osborn never dies in Spider-Man, then Harry never finds out, never becomes the new goblin and wouldn't be able to save Peter in Spider-Man 3?
Answer: Potentially, but there are way too many variables. Changes to the original Spider-Man timeline might have such ramifications that the events of the third film never come to pass at all! Or indeed the Norman Osborn that we see might be a variant of the one in the Spider-Man film, with his own timeline, or indeed making changes to the original timeline might split off multiple alternate timelines. There's just no definitive answer.
Question: Peter, MJ and Ned were all rejected from MIT for their associations with Spider-Man, so why wasn't that the case with Flash, who wrote an entire book about his supposed close friendship with Peter?
Answer: Flash is shown to come from wealthy parents. It's possible they made a large donation to MIT and/or are influential alumni themselves. Writing and publishing a book also isn't something that happens overnight. He could have been accepted into the school before the admissions board even knew about the book.
Question: Once cured and returned home, won't some of the villains, like the Lizard, still go to jail anyway?
Answer: More than likely... but that doesn't strictly matter. They'll still have been cured, avoided death, and "saved" in a sense. Even if they lose their freedom, they still are going to have a happier ending than they would have otherwise.
Remember that Oscorp is a corrupt company in the Amazing series. More than likely, both Connors and Dillon might be killed in prison under orders, so some happy ending.
That's a very bold assumption to make, especially considering they DIDN'T kill Connors after the events of the original "Amazing Spider-Man." At most, Connors will remain in prison. But I don't even know about Dillon. There's an exceedingly high chance he could just walk, especially presuming he'd be teleported back to around the time he was originally killed, and the world would think he's dead.
Question: The miscast spell made everyone who knew that Peter Parker was Spider-Man to appear in Tom's universe. Why didn't Mary-Jane, Harry Osborne and Eddie Brock from Toby's universe and Captain George Stacy and Gwen Stacy from Andrew's universe also appear as they knew Peter Parker was really Spider-Man?
Answer: Perhaps they did cross over, but they were not part of the plot, so we just didn't see them. They were all returned at the end anyway.
Answer: It could be there were too many characters and too many subplots already, they only needed the characters that would cause the most damage to Peter's universe. There are confirmed sequels in the SCU and The MCU, who knows who could show up there.
Answer: His spider-sense is probably somewhat aware that his astral form has been separated from his physical body, so it is taking over and controlling his movements.
Phaneron ★
I concur with your answer because while he is separated from his suit you can see the aurora of his spider tingle all around his head.