The people here can help get the drains and water supply in correctly, but I highly recommend you check out www.johnbridge.com for building the shower.
You do NOT want the pvc liner directly on the flat slab. Nor do you want to use any cement board (cbu) on the slab.
A traditional liner and mudbed shower can be made with any size doorway. To seal around the edges that go over the curb, they make corners that you glue in place with the pvc cement.
An alternative that I really like is a surface applied membrane - Kerdi from www.schluter.com. This will make the entire shower waterproof, and you only need the single layer of sloped floor. With a 3x5' shower, Schluter makes a tileable pan that you just set in thinset on the floor that would be quicker, but it is less expensive to do with deck mud. I used one of these to build a shower for my mother and it worked out well. It was faster than a mudbed, and I live 400-miles away, so was trying to get it done in one trip. Had problems with other things in the bathroom (moving the old cast iron plumbing for the toilet, etc.), but the shower went in fine.
There are some methods to build a shower properly, and lots of wrong ways. You really want it done right and that requires the waterproof liner to be sloped to the drain. Check out John Bridge's 'Tile Your World' website for help, you'll be pleased.