you would need to push it or pull it.
cart+steam engine
Cart and combustion engine makes car
tool + wood= wheel, wheel + wood = cart, cart + combustion engine= car if you don't have combustion engine it's boiler+coal= steam engine, steam engine + gasoline = combustion engine.
cart + combustion engine = car steam engine + gasoline = combustion engine boiler + coal = steam engine
put in a faster engine
nitrous and a bigger engine
That would be illegal. You would have to make your own account.
This is difficult to answer without knowing the make of the car or engine but an average engine would cost upwards of $300 but for an antique engine you may need to go to a specialized dealer.
Only if you make it from materials that float, but then it wouldn't be a go cart, but a float cart. It wouldn't be heavy enough to stay on the road as a go cart.
You can not make a golf cart legal for public streets because a golf cart is incapable of protect it's occupants in a two vehicle crash. In order to be street legal it would have to pass it's crash tests and be judged safe for it's occupants. Obviously you can't build a real golf cart that would pass those tests.
The Engine might rev a Little higher , which might make the go-cart go a Little faster - or blow the Engine up.
As you don't give engine make and model , difficult to say. Possibly around 8- 1 comp.