Issue 1: A groove would leave a little over 1/8" on either side of the plexiglass. I wouldn't go the full 3/8" deep on that, as it probably isn't needed since it is plexiglass, and will also make that wall material a little less brittle. It is still a little thin, but as long as it doesn't get abused, will probably be okay. That said, if it were me, instead of a groove, I would set the plexiglass in a rabbet so that it can be installed/uninstalled after the project has been assembled and finished.
Issue 2: The only reason to do a T&G for the back panel is to help make the boards line up. Since it is a long grain to long grain glue up, you will have plenty of glue strength without the T&G. You may want to consider having that back 'float' in grooves in the back to allow for wood movement.
Issue 2: The only reason to do a T&G for the back panel is to help make the boards line up. Since it is a long grain to long grain glue up, you will have plenty of glue strength without the T&G. You may want to consider having that back 'float' in grooves in the back to allow for wood movement.