I'd see Shadow as a bit of a Batman-type character in the games, so I'd guess he'd be sort of the same way in the show, albeit a little corny or over-the-top. Maybe as a protector of the space station or something.
Yeah it could've. In fact, I found that some of the things in the old Sonic shows came later in some of the games. It's almost like they foreshadowed a lot of what would happen in future games by doing this.
I can see Shadow questioning Mamma Robotnic about Maria considering Mamma Robotnic is Maria's Aunt.
I'm planning on including a confrontation between Mamma Robotnic and Shadow in an RPG if my partner ever gets around to responding faster. Mamma Robotnic would tell Shadow some disturbing facts about her and the death of her neice.