It certainly does increase the flow of the display setup but bear in mind that if you actually want the pump to do real work eg lift water to a head or against a restriction then it will have an adverse effect as the engine has less mechanical advantage.
Probably not. As we saw with the direct drive, the engine could be run at, hmm, let's just say very fast, without the pump giving a huge output. Geared up, the pump is giving a good flow rate at modest engine rpm with very little head, and we are told the engine is well on top of that delivery at this gearing.
Centrifugal pump behaviour is nothing like a positive diplacement pump. From no head, or next to none, as we have here, as the head is increased, the pump will come into its 'design' range, where, for a given shaft speed, flow rate x head is maximised. This is the condition at which it will absorb the greatest power (at that speed) even though it is working at its best efficiency. Note also that flow rate x head = power output. If the head is increased further, the flow will start to decrease faster than the head increases, and the power absorbed will be less.
Increase the shaft speed, and the pump will deliver greater flow at no head, and greater head at no flow. If you increase head and speed commensurately, so as to stay on the max efficiency duty, then the power absorbed increases as the cube of the speed. Roughly, the flow is proportional to the speed and pressure proportional to the square of the speed.
All of the above is generalisation, and describes a pump that is well behaved. Some designs can be unstable under certain conditions. The Stuart No 1 has design peculiarities, but I don't have much idea as to how they would affect the performance characteristics in practice.