I'd actually like some information about building the base for laying tile around a pool.

Hopefully someone who builds pools, or someone who's recently had tile decking installed around a pool, will be able to provide some info.

My main questions are about the thickness of the concrete under the decking, control joints, gaps between the coping and the decking, amount of slope of the decking, what type of drainage systems to use, and things like that.

Anyone?

There are two ways to achieve your goal.

1st- would be to remove the existing coping, concrete, and the paved patio. Replace the coping and use a stabilized subbase under 1 1/4" travertine pavers or pour new concrete in these areas and cement on a 1/2" travertine tile (more expensive)
2nd- would be to use a travertine overlay coping where you cut the bullnose off of the old brick and cement your travertine tiles over the old concrete and paved patio (less expensive)

I prefer either of the first options because you stand the risk of more lifting/settling when thinsetting down to your existing broken concrete deck.

If you go it on your own post any of your questions here and I and the other builders would be happy to assist you.
Trust me on this, you can save major coin doing it on your own. This isn't rocket science!!!

See ya,
Kelly