@raspberrypi9 typically one needs a small computer to fit in a case on the wall. there are quite a few SBC (single board computer) capable.
yes to your components list. and wherever you can find them in your budget. mirror glass is the most expensive component .
i have wanted to cover my 55 in tv mirror, but $1000 incl shipping is out of the budget for that .
touch yes. they make ir frames that go around non-touch, and send mouse cricks to the app.
note: very little is touch enabled.
oh, and you do get fingerprints…,