You will have to do it in stages. I have a corner shower that I redid. On the big gaps, put a base bead in, then leave it alone to dry. That’s how I did mine. Obviously take that old caulking out, clean it, then start over.

Yes you can do that, just wire it back up the same way. Put the single black on the top screw, and add a pigtail to the two twisted wires (add a wire and marette to the two) then put the pigtail to the other screw. Easy peasy!