I will propose a solution for each task:
1. A Node server controls the music, and is in turn controlled from a served page, allowing those with the appropriate credentials to control the music from their device and forgoing the need for dedicated interface equipment.
2. There are multiple open-source utilities regarding audio normalisation. I recommend Sox, which can be called by server to normalise audio files whenever they are uploaded to it.
3. A raspberry pi powers on whenever power is supplied. By configuring auto-login and adding the server to the startup script, along with regularly saving state, this effect can be achieved. Tying the server to a cron job will allow it to turn on/off at regular times.
4. I propose a programmable playlist system, where each playlist has a set of rules regarding the current time, with adjustable priority. If the rules fit, the playlist is added to the play queue according to its priority.
5. See 1.
6. By virtue of 1, each installation is independent to the Pi it is installed on, allowing you to install it to as many Pis as you own.
7. Should be simple enough, although there may be compatibility issues with 4.
8. Should be simple enough to implement.
For 7 and 8, I don't think they will fit with 2, since normalisation is not instant and thus files cannot be normalised as they are streamed from the server. I recommend that some integration is made to store normalised files there.