White and black counts as colours, look any gameboy game for reference and you will see only 4 colours at any time. Any shade or modification of a color counts as a different color. And for question 3, this is a jam. It's not a competition for any prize or something, we're making games for learning/fun and because we love to make them! So there's no point for starting right now to make a game for the jam.
And you can use Godot and export to any platform, you don't have to create a cartridge.