My Pelton Wheel works because a large pipe carries carries a large volume of water to a small nozzle increasing pressure.
It does not. The pressure would be the same regardless of pipe size. The nozzle on a pelton wheel is just there to make a directed jet that can transfer force better to the wheel cups. It doesn't actually increase pressure.(Pressure actually falls with an increase in water speed, a side passage on a nozzle would actually suck water into it, this is how things like paint sprayers, sand blasters and carburetors work)
The difference is that water flows easier in a large pipe, than it does a small one. So a large pipe leading to a small opening can maintain pressure under flow, better than a smaller one. It won't however increase pressure when you reduce the diameter.
A dam is a funnel. Funnels are used to change both pressure and speed.
One can simply compute the torque required to turn the generator and compare it with the pressure of the incompressible water to figure out what energy may be extracted.
Without the funnel, the water would simply go around the propeller -- taking the path of least resistance. (Assuming the generator requires some torque.) But if you dam it up in the funnel it can be forced to turn the propeller because the column of water pressing against the funnel's opening exerts pressure.
Negative.
Lets say its a one foot wide water wheel. A ten foot river, with a damn and a 1 foot opening, will exert no more force on a water wheel than a one foot wide river leading to a one foot wide water wheel.
Or for that matter, a one foot wide water wheel placed in a river ten feet wide with no dam.
Of course in practice, the water has to go somewhere, so the water level would rise, which would give you more head, which WOULD give you more pressure etc and would lead to more force, but that is not because it's funneled. It's just increasing your head, the pressure comes because now gravity has a higher head to work with.
The REASON the water would rise, is because it can't speed up to the point where its now flowing ten times as fast because its 'funneled', its just flowing through an area 1/10th the size at the same speed it was before so the other 9/10s of the flow backs up.
Now, the difference in available energy between a 1 foot wide river and a 10 foot wide river comes from the fact that you could run a ten foot wide wheel in that river instead of a one foot wheel, greatly increasing your available torque, but you can't make a slow river into a fast stream without changing its drop.
The way to get power from a slow river is to use a very wide waterwheel/propeller, and then gear it up to a useful velocity. Of course the more gearing, the more energy loss.
Energy production is a real pain. The basic laws of the universe make it hard on a fundamental level.