1/2 in. Brass Push-to-Connect x 3/4 in. Male Hose Thread Washing Machine Outlet Box

Yes. Each handle is attached to its valve stem with a single Phillips-head screw. The handles are interchangeable.

Mine came assembled that way. Guessing it is the 'default' set-up from the factory

The outside diameter of an ordinary 2" PVC waste pipe is a perfect tight fit. You could probably get by without cementing the parts together, but I did use cement.

Yes. Those two valves are what justifies the price. The valves include Sharkbite (or equivalent) push-to-connect fittings.

The existing 2" PVC drain pipe in my house was a perfect fit.

This box is: 8.75 in. (L) x 7.5 in. (W) x 3.5 in. (D). With the faceplate, this box is: 8.75 in. (L) x 8.75 in. (W) x 4 in. (D).

Put a wrench (this it was 7/8) on hex inside the box, then slip 8mm hex (Allen) into the end of the compression fitting. Unscrew as normal. Pop the knockouts on other side of box, then reinstall fittings.

Used to release the "quick connect" if needed. Use those or a cresenr wrench to help release connector. See youtube vid on how to release "quick connect" fitting.

Yes.

The strips that attach to the adjacent studs have a set of ratchet-like detents where they attach to the box, which allow you to adjust the box depth, however, you do not have clear access to this from inside the box. I believe they push in from the front, so you may be able to slip a shim in alongside the outside of the box at the mounting strap attachment points to hold it in place, and pull the box forward to see if it will advance a click or two as needed.