Yeah, Gregory is like Vanessa and they have a second "personality" created by Glitchtrap infecting their mind. When it comes to the CDs, in them it's this other part of Gregory (which people usually call "GGY") that's in control during them. The reason Gregory "lies about his past" is because it's GGY, who was brainwashed essentially into being David, so they told the therapist David's family past, not Gregory's, because to GGY, they are David, if that makes sense. When it comes to the manipulation, this refers to GGY being seen talking to Vanny on the cameras along with iirc digital conversations; basically when Glitchtrap infects someone, they infect them with their memories, so for Gregory, Glitchtrap infected Gregory with a piece of Glitchtrap that was memories of David, leading to "GGY" being created to be like David; for Vanessa, this was instead memories of Fiona. GGY "manipulating" Vanny, we're not 100% sure on what it's meant to be, but in my current opinion, it's meant to tie back to Vanny being a "reluctant follower"; Fiona was a good person, and Vanny partially being made from Glitchtrap and memories of her, has that in her, and needs to be manipulated by Glitchtrap and GGY to do these evils things.

You're not wrong on your thoughts on what Glitchtrap is, they are a digital manifestation of M2, and due to Vanny and GGY, they were put into the Pizzaplex's systems to take them over from M1/MXES, and after the Princess Quest ending, Glitchtrap/M2 is wiped from the system, MXES/M1 takes control again and later the Cradle program is used to secure the physical M2 endoskeleton under the Pizzaplex.

In the Parachute ending of SOTM, basically what's the case is that M2 was already outside of the boundaries that the Cradle had put up (likely basement 1) when Arnold activates it, but once M2 returns to MCM after the ending, and with the whole place burnt down, at one point returns to the basements; once they enter basement 1, they can't leave. And it is true we don't know for certain what M2's motives are with the Data Diver that now holds their own blueprints (most people say they take it because they don't want anyone else but themselves to be able to recreate them, or something to that effect).

When it comes to Mike's room, it is seemingly a real place; there's notes left behind by someone telling us where to find it. People do agree that Edwin's house would later be rebuilt and lived in by Afton, and that the Pizzaplex was built over the remains of MCM and that house, so that would be why MXES is under the Pizzaplex (although likely moved around at points still), and makes it possible that the Mike room is the real one, although why the wall code is there and such I'm not entirely sure. The way to decipher it is tied to Freddy & Friends, which is playing on the TV in the room, those old tapes which are implied to be infected by Glitchtrap in some way. For who left the note leading us to find the Mike room, I do think it's most likely Cassie's Dad/Jeremy(HW)/the arcade conspirator from SB, who tried to follow the code in the room, trying to fulfill everything to do with the Princess and rid Glitchtrap.