VNC should be the answer. Virtual Network Computing(VNC) is a graphical desktop sharing system that uses the Remote Frame Buffer protocol (RFB) to remotely control another computer. It transmits the keyboard and mouse events from one computer to another, relaying the graphical screen updates back in the other direction, over a network.
With VNC, you can control another computer or a group of computers available on a local network.
The procedure as follows: Install Real VNC viewer on your computer, and Real VNC viewer on your Android tablet. Your computer and Android tablet should be connected to the same network, if you don't have a WiFi connection, you can use your mobile WiFi hotspot or USB tethering to connect your computer for which you needn't require mobile data pack.
For your HDMI solution, I believe your tablet support OTG functionality. Buy HDMI adapter and an OTG cable. I believe it should do the job. I fear the HDMI streaming could go opposite, so VNC should be your choice as HDMI would drain the battery and you won't be able to charge your tablet in between.