Your post formatting is rather annoying, but I'll answer the questions anyway.

Game Style: Probably 3D Platformer - obviously, Jazz should have a gun, but it probably shouldn't be the main focus of the game. Other fun options would be Adventure or Racing. No cars, just zoom zoom jackrabbits.
Platform: Every single one!!!!!!!
Time Period: Probably Sequel. While a prequel would be interesting, it would probably be best to establish the characters we already have a little more first - Lori, for example, is practically an enigma.
Graphics Type: That shiny Sonic style might work well.
Multiplayer: Every single one!!!!!!!
Other Companies: I don't care who makes it, as long as it's good.
Cinematics: Probably lightly story based. I could be persuaded into agreeing with most any of the options here, to be honest.