I added some gopro footage to my trial version of premiere elements 11 (I tried .avi and .mov) formats but all the way through the editing process and after saving the video it appears as a double. i.e. there are 2 versions of my video side by side together rather than one. I've added a screenshot of what I'm experiencing. If this is just because it is a trial version fine but it's a bit annoying because it does not give me a true idea of what premiere elements is like, and I don't want to fork out for the full version not being certain I wouldn't face the same problem there.
You've got a couple of things going on here. For one, yes, the trial version is limited in its ability to work with certain video formats. Go Pro footge will definitely not work well in the trial version (and it may even cause some issues with the full, purchased version).
Second, how did you get the footage from the Go Pro cam to your computer? If you used any software other than Premiere Elements to get this footage from your camcorder, it may have converted the video into a format that is even further from Premiere Elements' compability.
As a rule, Premiere Elements is not your best choice for editing Go Pro footage. In fact, virtually all of the major editing programs are challenged by its unique format. Even pro editors.
Bill Hunt has some suggestions for working with this footage.
The best solution is to edit the video with the software that comes with the program.