Hi tariku,
Thank you for using the Apple Support Communities. We see you're having some issues with your mouse and a second display. We have a link with some steps that might be helpful If your external display isn't detected or appears blurry on your Mac.
Disconnect the cable from your external display from your Mac, then reconnect it. If the cable from your external display doesn't connect to the ports on your Mac, you can use a Thunderbolt 3 or USB-C adapter."
If this doesn't help, try setting up a temporary administrator account on your Mac and see if you can replicate the issue there. That will help to narrow the issue down: Set up users, guests, and groups on Mac
We hope that helps. Let us know what you find. Take care.