I mean when I check automatically fix errors or scan for bad sectors can that do anything bad to my system? It won't delete any system files?

In theory it can, but so can using the computer itself. Make regular backups, have adequate and up to date security and a firewall and you will be fine in case anything happens. I have automatic fix not checked because I want to see if there are any bad sectors happening, usually a sign that a harddisk is at its end of life.