Trying to replace double sink bathroom faucets from the 1980s and after removing setscrews tried to pull of handles after oiling them and using a Husky faucet puller. No luck with the Husky and no luck unscrewing the threaded pipe that attaches to the lower silver bell of the handle (it moves up and down the threads but not past the faucet handle). Am I missing something?
Are you wishing to replace all of the faucet for a new one or just the handles? For full replacement, there should be a locknut on the underside which needs to be removed and also the water line connections.
When in doubt, cut it out! If you've tried penetrating oil, a puller and maybe whacking up and down on the handle with a hammer (breaks any scale or rust locking) or blow torch (extreme heat expands the outer member) and nothing works.
Then, remove the underside's locking nuts, as seen in picture 2, and just cut them off with a reciprocating saw. If a locking nut doesn't budge, then cut a slot in that to then pry open and off with a screwdriver. Do not let it win!