How to root Teac Tc-7120
I don't know about rooting your device, but I can help with getting your device to be recognised by your computer.

Exact instructions will depend on what OS you are running, but basically you need to find the .android folder in your home directory, and replace the adb_usb.ini file with this one.  this tells your computer to let adb work with a load of different usb devices.  You may need to type this on the command line to get it to work after you do this:

adb kill-server
adb start-server


and now running this should show you your device

adb devices