Plumbers....adding a shower drain questions

The reason I asked about if you had previous problems was related to venting as Scott touched on. If it's not already vented it should be. Run it in the interior wall as he suggested. I'll just add that access is necessary with an AAV. They do fail eventually and let in sewer gas. Even a simple heating register grate mounted in the untiled side of the wall works fine.

The trap as you already know is mandatory. It's only real function is to trap water to block gasses. It does not have to be serviceable, and isn't meant to catch earrings, wedding rings, or car keys(that's the strainers job). It does need to be well constructed, and thought out though. Use sweeps and 45's to facilitate easier snaking.

Backflow/check valve. Unless you have a really strong, valid reason for needing one... don't bother. Waste lines only have gravity helping them and therefore can not overcome the spring assisted style. The water and waste will stack behind the valve until enough pressure is present to open the valve. The unassisted style just has a flapper that uses it's own weight and pressure/vacuum differential to open and close the valve. There's not enough velocity in a drain line to keep the valve clear. If for some reason you still really want one....do not burry it! Install a proper one on the main. Bust the floor out and install a service/sump box to mount it in. Also use the style with the clear lid for a quick visual inspection, and easy service.