Weird hidden folder and file on desktop as old as the computer, what for?
They are for deleting. They don’t ship with the os and aren’t worth worrying about since they are machine generated and you’d need to use the command line or a hex editor to examine the binary file for clues. 

If you’re super worried, set up Time Machine to back them up, then delete them. 

Your home folder wasn’t created until after you received your Mac and chose your short name, so it came from a program or transfer you made soon after this mac was customized for you.