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Adobe does not try to make Premiere Elements "backward compatible".  Each version is "stand alone".  You can leave the old version on your computer for re-editing old projects.   

That said, you may be able to open old projects in the new version.  It depends on what is in them.  Some effects, transitions, tools, etc may have changed.  If your projects are relatively simple, opening them may work.

Best advice is to make a copy of the old project before opening in the new version to remove risk of any corruption. 

To open that copy, go to File > Open Project and navigate to where you have the copy saved.