The OP specified 500kg and >10KW. The only pertinent unspecified variable is how far the weight gets to fall; i.e. how long do you get 10KW. You don't get to choose the minimum speed of the fall if you've specified the other stuff.
Once you've achieved the minimum speed, then you would want to control the rate the weight falls with gears and such, or store the extra power produced. But this will happen naturally with whatever energy extraction system you have. There will be an equilibrium speed that is determined by the power extracted. Of course there are kinetic energy issues with the beginning and end of the fall.
The basic point is that you don't have to know a lot about the details of energy extraction (alternators, gears, etc. ) to determine some significant limitations on what the falling weight has to do. I would strongly suggest a "black box" approach first.
Yes! But there are limits from the laws of physics that should be understood and evaluated.
I respectfully disagree. But we do believe in physics here. Maybe we are "projecting" reality. No one's saying this can't be done. Gravity batteries are a thing. People have built them, and they work. But, they do have to be designed within the limitations of physical laws.
Honestly, I think we are trying to help. When I say "study high school physics" I don't mean it as an insult, I'm trying my best to point the way to a successful outcome.