That is almost 3 feet by 3 feet so I would think you have plenty of room.

I agree, I think you'd have plenty of room especially since it folds up.

No.

If the bench is the right size, it should fit.

For smaller showers we like to install a 24" corner seat made by Better Bench. The corner seat is tiled and you do need to have blocking in the walls for support. It is a space saver.
If you still want the folding bench seat I would suggest cutting out a cardboard template the exact size and placing in the shower so you can actually see the amount of space it takes up. It would be a tight fit.