MacBook Pro mouse pointer moving by itself and more

Try an SMC reset and PRAM reset (hold the PRAM reset for a full minute so it activates several times).

Boot into Recovery Mode (Command + R) or Internet Recovery Mode (Command + Option + R). Does the Trackpad still behave erratically? If so, you have a hardware issue.

FYI, Defective trackpads can work normally for a while, but then begin to become erratic again after some use.

Erratic trackpad movement or an erratic cursor can be due to a defective Trackpad or a swelling battery. If a reboot doesn't work and these other things don't work, then you may want to take the laptop to Apple or an Apple Authorized Service Provider to be examined.

If you are in Internet Recovery, and see lots of disks, they belong to Internet Recovery, and are not a problem.

Internet Recovery creates over 25 RAM disks to store its working files, so that your drive can be completely free to be erased or installed on.

Have you tried shutting down the computer and restarting?