This is not a virus, but it's hard to say what it might be. Given the wide variety of problems, I'd be inclined to blame a badly corrupt hard drive and/or system. Possibly a failing hard drive. Do you have backups on a different hard drive, made with something like Time Machine? If not, that needs to be your absolute first priority.
Once you've got backups, my advice would be to erase the hard drive, reinstall the system and any apps that you rely on from scratch, then restore your data only from the backup. That may be more extreme than what is necessary, but with what you describe, we could potentially go back and forth trying all kinds of other things for weeks and not come up with a solution, so you may as well just "nuke and pave."