You really need to remove all those bad repositories and then run a proper upgrade.
Open Software & Updates and remove any repositories there that are showing an error in the "sudo apt update" results.
Once they are removed, run sudo apt update && sudo apt upgrade.
In the meantime, can you please shut Down the notebook completely. Make sure it is powered off and unplugged.
Take a q-tip
and gently clean the HDMI port on your notebook thoroughly. You can use a small drop of Rubbing Alcohol but don't get carried away and soak your machine.
If you have a spare HDMI cable, this is a good time to test with it.
Some HDMI Cables are Directional - one end is for the computer and one end is for the output. They cannot be reversed. So please Check Your Cables.
Power on the notebook and see if any graphics appear.
Then plug in the HDMI with the notebook still on and see if the TV displays the graphics. If it does, select shutdown in the app menu and then immediately unplug the HDMI before the computer shuts down.
Boot without the HDMI cable and test graphics on Notebook monitor.
Your Notebook Monitor itself maybe the problem.