Fountain--while it could be done in a perfect world I do not believe it would be feasible and the whole thing is so vulnerable to disruption.
Dragon's Egg got it very wrong, if one of your fountain bits misbehaves it misbehaves very badly. They're moving way above orbital velocity if they hit something that energy is promptly liberated. The Cheela couldn't catch those rings, they had to be moving at high relativistic speeds and would have hit with something akin to antimatter level force.
Orbital rings--only if you have elevators. Remember, the Ringworld is unstable. So is every other planetary ring.
I do not recall numbers on hooks so I will not address them.
The Moon has a whole different set of problems. There is no synchronous orbit, elevators must go above synchronous orbit, so the normal version can't exist. Nor can anything stand up to be yanked around by the Earth.
But there are two cases that avoid the yanking problem: pointed towards and pointed away from Earth. Current cables are good enough for a useful Earth-pointing cable. The free end dips below synchronous orbit, but it's moving very slowly. You do what people think rockets do--go up. It takes a lot less energy to catch the cable than it does to even reach orbit.
How to have such a cable in an environment with geosynchronous satellites is another matter...
There's also another interesting cable situation. Cable on Mars? Iffy--and those two moons would be a major problem. But flip the problem over--put the cables on the moons. The low end dips into the atmosphere at aircraft-type speeds. The cables can toss to each other. The high end can capture/eject to Earth or the asteroid belt.