I'll take a stab at some of your questions.
Unless I misunderstand, I don't see how you would do it otherwise. You need at least a little room to work with.
Depends on regulation in your state. I don't know Nevada rules. In WA where I live, anything over 25 years old doesn't need to be emissions tested. I believe in Cali, you would need to keep all of the smog stuff and getting it tuned well. I am building my engine desmogged, and learning as I go...it is a 3FE though. There is plenty of info on the forum on desmogging and even kits you can buy to help I think. I don't know enough about it (yet), but if there is no belt hooked up to the air pump, you certainly aren't running it properly.
I assume you are referring to the smog system. I would have said you can't partially desmog, but since your air pump isn't hooked up, maybe you can. But I would say generally speaking, your engine won't run nearly as well if you don't either have it fully desmogged or fully "smogged".
If you are going to lift the engine and mess with motor mounts, I would say 100% yes remove this stuff. It isn't too hard. But given the work you are doing, I would for sure even if not moving the engine. I remove my fenders whenever I am doing any work...its just easier to get in there and maneuver around.
You can take your radiator to a radiator shop and have it cleaned and pressure tested. They will tell you if it is still usable or not. I would suggest doing that...getting the cooling system working at peak is essential. Especially in Nevada, I wouldn't mess with overheating.
I'm enjoying your thread and learning as I go as well.