I wanna use my friend steam back up file (he backed up multiple games into one folder) but I don't own all the same games as him. I want to back up a specific game from that file folder. Is this something that is possible to do?
If your friend used Steam's Backup feature, you should be able to restore just some of the games.
If your friend just made copies of their Steam folders, you can just not copy back the folders for the games you don't own.
Having said all that, if you have the free space, you can just choose to restore all of the games; Steam will replace the Play button with a Buy button for the games you don't actually own. You can still use Steam's UI to uninstall these games.