A giant floor sander, along with the sandpaper and buffing disks to actually use it (extremely expensive, not sure if easily rentable)
No, it will pretty much only look worse if you try to do it in patches. Also, depending on the wood, you may want to do pre-stain treatment, cause some woods just absorb stain really splotchily.
Depending on the finish, could be anything between a few hours to a couple days needed between layers of finish. Some require a month or more of curing before you should put furniture on top. I’d recommend against those, we have more modern finishes that are honestly just better in addition to being more convenient, despite what some people say online. YouTube side by side comparisons are my go to for finding info on this sorta stuff.