1. Considering that the resolution of the Genesis was more of a product of the system and TVs at the time, I would say go widescreen.
2. I'd be down for a slightly shorter adventure. Something that while having fewer zones, has more of a Sonic 3 style where they're jam packed with goodies to find.
3. N.A. I don't care if they add a dozen new characters, just don't make them stupidly bland to the point of only appearing for one game and then never again.
4. Sonic 3 = Brand New Sprites. Sonic 4 = Sonic 3 sprites, Edited Sonic 3 sprites, or Brand New?)
I don't think sprites be used in the sense you're speaking of. Legacy styled sprites are for retro styled games, which Sega hasn't really toyed with doing, to my knowledge. If they were to use them, I'd say something in the vein of Rayman origins where they're hand painted and placed into the game. Would definitely make the game's scenery look different too.
5. N.A. because I can't really decide. Both look good, so whatever I guess.
6. Sonic 3. I like the idea that the ending screen of each act is the starting point of the next, and how each zone flows into the next.
7. What would be the point? Sonic 2 and 3's multiplayer show that it just isn't that good of an idea. Too hard to keep track of the players, with local you have to deal with splitscreen that either cuts your view or horribly shrinks it, and you have the problem of one player either being invincible or having to share rings and items with them.
8. N.A. as I haven't played the remakes and don't intend to.
9. No. His only real trait is that he's slightly slower than Sonic (if that) and can fly. Can't really do much with that unless there are a lot of vertical shafts.
10. Depends on if he would even be in the game at all, and if he would have a separate storyline if he was.
11. Green Hill Clone. Every main classic Sonic game's first zone always expands upon the Green Hill Zone idea in a new and exciting way. (Emerald hill with the corkscrews and caves; Palmtree Panic with the giant 3D loop and speed tunnels; Angel Island with the miniboss setting the forest aflame; Mushroom HIll's seasonal gimmick and first ever running boss of the series.)
Of course, I'm also fine with Sonic 4 as it is. Sure it wasn't very fun to play, but it's definitely an interesting piece of history for both the fandom and Sonic Retro.