if a cart/vehicle has to travel along a flat surface, with the rotational energy provided by a rotating axle, how could i fix the rotating axle to the cart, and the wheels to the axle?
The force of the rotating axle will induce an equal and opposite reaction on the cart. This force will be a torque or twisting force. Look at the engine mounts and figure out a way it can be mounted to the cart to resist this twisting force. The fasteners or weld required will depending on how much torque is produced. In general bolts should be strong enough but you need to determine the number of bolts and the size (diameter). This is a general answer but the question is general too.
Find a small trailer manufacturer in your area and go there to see how they do it. Check in your yellow pages.
