Could the rotation of a black hole cause other planets to rotate? Because everything rotates so perfectly, and we know that some blackholes rotate and they're the biggest things in the universe, so a silly question comes to mind.

If you remove all black holes from a galaxy:


Would it still rotate?
Would the rotation of the planets inside it slow down until there's no more rotation/gravity?


I imagine that the black hole has something to do with the fact that we have gravity since it's always rotating and pulling spacetime fabric inward like a tornado. There are 100 million black holes in our galaxy so I think of them as rotation generators.

Last year I read a research paper that the rotation of a black hole can't cause gravity, but forgot why.
A rotating black hole (or indeed any other rotating object) can cause nearby objects to rotate through an effect called frame dragging. However this effect is really small! Detecting it requires either a a body to be in a pretty close orbit around a black hole, or extremely sensitive instruments.

The fact that the galaxy and almost everything in it rotates in one way or another is not considered to have anything to do with this effect. Instead it is basically the rotation left over as clouds of gas, dark matter and later dust collapse under their own gravity. Inevitably they do not fall exactly straight into the middle of the cloud, but end up aiming off to one side or another and so orbiting around the centre, and the final spin of the collapsed object comes from the more or less random overall total of these spins. Objects spin so fast because very large clouds of gas and dust have collaposed to form fairly small objects like planets and stars, and just like an ice skater speeding up their spin by pulling in their arms, this speeds up the spin of the central object. 

If you removed all the black holes from a galaxy there would be no major change. A shift in the orbits of stars, especially near the centre of the galaxy and some changes in the behaviour of the clouds of gas between stars as the radiation from the central black hole stops acting on them.