When taping cement board do I need to tape at the walls?
The cement board must be properly backed at tub edge to keep it stiff. The gap between it and the tub is grout filled. I don't tape corners. I do tape bevels simply to make a flush surface for the tiles. I generally silicon tiled corners. I use 1/8 inch gap and that give me more room for silicon on the corners. That's enough room. The idea is to avoid buckling from settlement and let you get more silicon in there. 

You will notice the bevel edge on 2 sides of the cement board. When butt end joints are required it's a good idea to rasp a bevel into the ends using a wood rasp. The idea of the bevel is to allow you to get more joint compound in there making a stronger joint. The minimum for tub joints is Fast Set. It doesn't rot. 

I silicon tub ledgers to avoid future squeaks. Just because you screw or clip the tub to the wall doesn't mean it won't squeak later if settlement occurs. Yes, fill the tub full when setting it.