Game Style:
2D jump'n'run. But with more than the previous games. Better weaponry system. Maybe you could even gain experience, making it a little like an rpg. Something like being able to increase your hearts like in Zelda would be neat.
Etc.

Platform:
PC. Mac. And anything else that could support an easy-to-use and yet advanced level editor like the JCS. Only better. Ooo.

Time Period:
Sequel. Definitely. ( ++PLAYING AS EVA =D=D )

Graphics Type:
Just like before. Except more 3D-looking, despite the 2D nature of the game. More realistic and less cute than Banjo-Kazooie, but still cartoony.

Multiplayer Types:
Yes, indeed.

Companies:
The firm that made Earthworm Jim! =D
Either that, or an unorganized group of Dutch students.

Stories and Cutscenes:
Plot-based, plz.
But not so much that making an own episode would be incredibly complicated because you'd have to set thousands of switches and stuff to keep the story going. Just... conversation with NPCs and the like and neat cutscenes, like in JJ1, except animated, and all is well.