You can't get past the bridge sequence without triggering it in singleplayer, there are invisible walls. Also you can do a regular playthrough in multiplayer mode, just the special stages are different.
I don't really know what you mean by that, do you mean singleplayer, or just going through the game like normal in the multiplayer co op mode, just by yourself
So I was looking around in the wip thread for soap for some reason, and in a couple of the gifs, soap had a spindash sprite. But he doesn't have it anywhere in the final release. What happened to it?