Basically any remote desktop client will do what you're asking. Miracast is a good one, google makes a good one... I don't know which ones will work on tablets; do a little research, but that's what you're looking for.
Hyper V is a virtualization client if you're running virtual operating systems. (Think using Wine to run windows within Linux.)
There's no benefit to upgrading, don't worry about it.
Hyper V is Windows 8.1's built in Virtual Machine software.
Much like Virtual PC for Windows 7, but with a lot more features and functions.
It requires a CPU that supports SLAT
Open CMD and type systeminfo. Next to Hyper-V, all of them have to say Yes for it to work.