What computer operating system is involved?
Some of these older programs have features that have been removed in the later programs.
So, in that sense, good idea to keep them active on the computer if you have room for them. And, I would not remove any prior version until you have given Premiere Elements 13/13.1 a good workout.
Premiere Elements versions are standalone versions so deleting one version should not affect the others.
When you do decide to remove a version, I would encourage you to Deactivate it from within the program before you Uninstall.
Deactivation and Uninstall are not the same thing. In Premiere Elements 8.0/8.0.1 and 10, see Help Menu/Deactivate. In Premiere Elements 12/12.1, see Help Menu/Sign Out.
Any questions or need clarification on the above, please do not hesitate to ask.
Thanks so much for all your info. Greatly appreciated!