I was recaulking my shower/tub, and noticed that some tiles were
loose. I pulled 3 tiles off the wall, and saw that the wall board
(I'm not sure which type) had some water damage.

I see plenty of sites describing how to fix this, but I have some
questions.

The rotten board surrounded the bathtub spout. I assume it's a best
to install a single piece of new cement board, with a hole cut for the
pipe. Is it easy to unscrew the spout without causing further
problems? What will seal the pipe connection when I reconnect it?

Or should I just install two horizontal pieces, on the top and bottom
of the pipe?

The tub spout pipe came through a tile that had been cut in half (or
maybe broke at some point), and then had a hole cut in it. Can I seal
the crack between the tile halves with grout, even though the crack is
smaller than a standard grout joint?

http://www.thisoldhouse.com/toh/arti...218790,00.html recommends
avoiding vertical seams, by removing entire horizontal rows of tiles.
Other sites just recommend removing enough tiles so the patch reaches
two studs, and so the outermost tiles are half on existing, good board
and half on the new board. Is that enough?

Behind the wallboard is fiberglass insulation with a vapor barrier
(even though it's an interior wall). The vapor barrier has some cuts
and rips. Is there a way to install a barrier patch over just the
exposed section, rather than the whole section of wall? What material
should I use?

I see you're supposed to leave a small gap between the bottom of the
cement board and the top of the tub. Why? If water gets through the
tiles, where does it go once it's on the front of the cement board, or
the front of the vapor barrier?

Jimmy