Sharing Mac mini with monitor in another room. (also bluetooth keyboard/mouse with second monitor) My 2012 Mac mini/thunderbolt are in one room 
I want to sit in another room and work on the Mac mini. I have a second monitor and bluetooth keyboard accessories. I do not want to set up a second computer, but I do have an iPad.

Can I work on the Mac mini from this other location, and does the remote monitor have to be hard wired. If I had to hard wire, would setting up ethernet connection work? The benefit of the ethernet is that my house is prewired, so I would be able to work from several rooms without moving the Mac mini from its office setup.

For now, we would not be using the TV or a second user on the mac mini at the same time as the remote location. The remote location is mainly surfing, email, minor document projects etc. I have an iPad but also a second monitor which i'd like to put to use and it is more enjoyable and convenient w/ bluetooth keyboard/accessories at the fireplace location.
A couple of options for you...

You could use an Apple TV connected to your monitor and connect to your Mini using AirPlay - since 10.9 you're no longer restricted to using AirPlay to just mirror your main display, you can use an AirPlay-connected display as a secondary display.

Otherwise you're looking at a hard-wired display setup. Hard-wiring may be cheaper, it all depends on the length of cable-runs as you may need to look at active video signal boosters/extenders for longer runs. If your existing Ethernet cabling is point-to-point and you've a cable that runs from your main room to your secondary, you could use DVI-Ethernet extenders. These use the cabling to transmit video directly rather than actually being connected to the home network.