Using Mac Mini without keyboard and monitor

Yes.

I have a similar setup with my Mac mini, since I use it as a web server. I can remote in just fine with TeamViewer

@hcsitas, Teamviewer is free for non commercial use. And there are several other options that are free too. LogMeIn is a paid product however.

1. No. The Wifi needs to be set up.
2. You'll need them for initial setup
3. If you are Remoting into it from a Windows PC, then yes. You'll need something like Teamviewer or LogMeIn or similar installed on the Mac.

If you were remoting from a Mac there's Apple Remote Desktop, but it needs to be setup first.

1. No
2. No
3. Not possible, unfortunately

Yes, as long as you pay the monthly/annual fee (prohibitive imo).

Not really: "TeamViewer is proud to support our non-profit community. Please contact our sales team to see if your organization qualifies."

That to most people means No. Marked helpful nonetheless.