Welcome, @torc! You might also check out this thread from @3DPrintedWaffles.
- Automatic timed shutdown and boot up (no point it being on at night when nobody is there to benefit).
This requires added hardware, as the RPi doesn’t have the internal capacity. See this thread on StackExchange. Given you’ll already have the monitor going into standby, you’ll need to determine whether the added cost, work and potential complications are worth the effort.
- motion sensor to activate display.
@cruunnerr is the village expert. Check out this very thorough walkthrough to get started.
- small LEDs on back of frame that change with certain outside temperature changes.
You can start at this post and module. However, there are endless articles on how to connect an RBG LED light strip to an RPi, etc.
- map display of selected mobile devices by clicking a button on another device (eg if I want to see where my kids mobiles are, click a button on mine and a map would appear in the mirror with theirs.
You can trigger displaying modules via a phone/tablet/computer with MMM-Remote-Control, or a button with MMM-Buttons – both by @Jopyth. The harder part will be the map. It’s true that Apple and Google have something like Find My Friends (or Find My Phone for devices connected to your account) but I don’t know of any available APIs for those services. (There are apparently some unofficial Node.js clients.)There is tracking software you can install on Android, but it tends to be insecure garbage.