Is the hood (bonnet) half supposed to lay over and fold flat on the opposite side?
No. It is supposed to be suspended above the other hood and not contact it. If yours lays flat you need to make sure that you have both an inner and outer hinge cap at each end and that they are secured to either the radiator or wood frame appropriately. Many times loose hinge supports or the missing inner hinge cap will cause the hood to lay flat when open. This will damage the hood.