Premiere Elements versions are standalone versions. You can have more than one version on your computer at a time. Just use one at a time.
I would suggest that you assure that all is well with 13 and its 13.1 update before you deactivate and uninstall 8.0/8.0.1. Deactivation and uninstall are not the same. To Deactivate the program, go to the opened project's Help Menu/Deactivate. More on that if necessary. To uninstall, use the usual Control Panel way if you are using a Windows computer.
What computer operating system is involved?
Best wishes with your video editing.