New house. Master bath needs some help. Diverter valve is fubared. Not sure what type I'd need in order to replace it.

I also would like to replace the hardware for the faucet (handles, spout, shower head, etc.). No idea what this style is called or where to look. Any tips on removal would be helpful as well.

Lastly, I'd like to replace the hardware for the jet tub. I don't know what brand it is and can't find markings anywhere. Suggestions? Is it even possible?

Yes, I know the tub is gross, I just ran everything to start to flush the system and realized that is a waste of time right now.