Borrow a USB mouse from someone to use while troubleshooting this problem.
There is no keyboard command equivalent to shut down and/or restart the computer.
Since a simple reboot of your Mac doesn’t fix things, see if the problem still happens in safe mode.
How to use safe mode on your Mac - Apple Support
Safe mode will often correct weird software behavior by forcing the OS to do disk repair, clear caches and other housekeeping and temporarily disables third-party mods. When you're in safe boot, the machine won’t be at its best performance, especially with graphics, but that's expected.
Does the same thing happen while in Safe mode?
You can exit safe mode by restarting your Mac normally, then reevaluate the problem.
If the problems remains after a safe boot, please run an EtreCheck (free) evaluation of your Mac and post the generated report back here in a reply. EtreCheck is a safe and highly regarded utility from a trusted developer and respected ASC contributor. The diagnostic report will not include any personal info. It simply gathers specifics about hardware performance and installed software that might be in conflict with the OS.
Please navigate to EtreCheck.com to download the utility. Be sure to Allow Full Disk Access when you install the app. Once you’ve run the app and created your report please post it with your reply to this message.
Please note you must upload the full report. To see how, please click > How to use Add Text when posting… EtreCheck Report.
We’ll use your EtreCheck report to look for the things that may be causing your problem and advise how to correct them.