You don't need the lath for Cement Board. CB on curb is a weaker system, but probably a lot easier for a DIY. You should use some fiberglass tape mudded with thinset at all changes of plane.

Okay. If I use the lath should I put some tar paper on the 2x4 prior to putting on the lath? And does the tar paper and lath need to extend into the shower prior to putting in the mud bed?

Tar paper or plastic, anything to keep the 2x4's from drawing the moisture out of the mud. I would extend the lath all the way to the floor, but there's no need to put it on the floor. Just completely wrap the lumber and staple/nail it down good. Be prepared to do your curb immediately after the floor if you can. It'll be easier and probably turn out better for you.

Don't expect perfection on your first curb. If it's a little out of shape the high spots can be sanded off and the low spots can be filled in. Try to keep the sides flush with the CBU (1/2") and the top slightly slope toward the inside of the shower. Don't overwork the mud, it'll just make it wetter and harder to work with. If you have a piece of 1x4 or 1x6, that's usually a little better than a steel trowel.

What the heck, I'll give it a try, gone this far no sense in stopping now.

Drywall. Can I use regular drywall in the bathroom or do I need a waterproof/resistant kind? Again, the shower has CB for the tile but I'll be tiling about halfway up the walls in the rest of the bathroom.
Leveling floor. The slab has a few dips. Should I try to level these before I install the the floor tiles or just level the tiles as I go?