That's the hardest part. Must get the correct angles to drain. If you are doing a standard size you can buy a premade bottom, but that is one area I always use a pro if tiling.
It also needs to be waterproof. I would start with a grenade base that you could tile.
Yes, that's how they were done for decades. Just make sure you get it waterproof and I would recommend using cement board to cover the framing and then follow it up with material specific for shower pans. Sort of like a vitchathane product that is super sticky.