when putting down cement backboard on the floor for tiling, can you just nail it down and skip mortar or adhessive?
You should use both screws and an adhessive or mortor. Without adhessive or mortor, your floor will likely over time begin to make noises and could cause grout cracking due to settling. Mortor is cheap and quick. Good luck!
I always use screws to hold down the backer board.
You should use screws to adhere it, not adhesive. the screws will pull the floor and backer board tightly together. They make screws specifically for this. Make sure you screw them down all the way before tiling, or the tiles will be uneven and possibly crack.
You could but you better nail or screw extra heavy. The chance of problems occuring are far less if you adhere the cement board to the existing floor.
A lot of tile installers simply nail or screw the backerboard to the subfloor without any mortar. You can get by with this technique if your floor is very flat. I always apply a thin layer of mortar beneath the cement board to fill any voids and compensate for minor unevenness in the floor beneath. This is good practice, but not 100% necessary. It isn't hard to put down a little mortar, use an 1/8 v notch trowel.