1. Let's say we could actually harvest all of this. Would it _actually_ be worth that amount? Once it gets here, wouldn't we have so much of it that people would be trying to give it away?
2. Would this impact our rotational speed at all? Is it possible that adding mass could slow us down?
The asteroid in question is only ~120 miles in diameter. Not massive enough to effect earths orbit that much. Earth is hundreds of thousands of times more massive.
However, Platinum group metals are relatively rare in earths crust. This would be the what we would really want from an asteroid. If it was just for iron and nickle not many people would think about asteroid mining.
There is unlimites solar power in the asteroid belt, 24/7.
If you were really desparate, a solar furnace could vaporize mine tailings and accelerate it through a nozzle for thrust. It wouldn't be efficient, but it is pretty much free, (except for shipping and handling). Kind of like that classic black and white movie where they are breaking up the wood of a box car to feed the steam engine pulling the train.
It would probably be better to use nuclear. The energy density is high so you don't have to launch as much material to get your mining infrastructure in place.
For 2., I think there's a good case to be made for a lot of that metal staying up in space as opposed to dropped and then launched back up eventually. In the long long term, isn't it reasonable to assume that Earth may end up losing mass due to space launches? Here's my corollary to your question for whoever comes along to answer: Is it possible that lessening mass could speed us up?
Earth masses 6e24 kg. SpaceX Starship can carry 1e5 kg. Suppose a MILLION fully loaded Starships launched EVERY SECOND, starting now.
It would take 20000 years of that for earth to lose 1% of its mass.
No. It is much more likely that Earth would become a long-term importer of space manufacturing for quite some time. It is much cheaper to drop stuff down into Earth's deep gravity well than to hoist it up into space. Pretty much everything in orbit (except for the Moon and mass where the Moon's gravitional influence dominates) will eventually come back down to the Earth's surface, too