Letters getting inserted randomly as I type. Has this ever happened to anyone?
Yes this happens due to several causes. USB hub issues (there are several internal “hubs” that can fail - liquid damage is a likely cause, but not the only one). Connecting faulty or failing usb and Bluetooth input peripherals is also a likely cause until you rule that out. 

Lastly, software automation could be a far less likely cause. Booting a brand new OS on an external drive might be a good way to check for that rather than erasing and reinstalling your Mac.