For the bathroom floor use thinset spread with a 1/4" notched trowel as your "glue", then screw.

In the shower, no cement board under your shower pan.

You can use a preformed shower pan, 36" square is a very common size. Do a google search for "36" shower pan" and you should get quite a few hits. They come in different types of plastic, in Swanstone material, there might be a cast iron one out there too but I think Kohler's cast iron receptor is 36" by 48".

If you want to build your own, Harry Dunbar has a nice pictorial showing how to do it with a conventional membrane here.

There are also tole bases made by companies like Schluter. Noble, Wedi, etc, but they are shower "systems." You use their material for the base and walls. Here's a lengthy thread with lots of photos a DIY deck mud preslope covered with Kerdi, as well as a complete Kerdi shower.

There are myriad ways to skin this cat.

Mongo