The answer to your question
Is it possible to remove watermark without purchasing the full version
You need the purchased version of Premiere Elements in order to remove the Adobe watermark from the tryout project file.
And, you cannot remove the Adobe watermark (purchased product or not) from any export from the tryout version (applies to export to file saved to the computer hard drive or burn to disc product).
Thanks for the follow up.
Any chance that your computer has a free video editor that you can use for this one project - Movie Maker 2012 for Windows or iMovie for Mac?
What is the destination for the project - export to file saved to the computer hard drive or burn to disc DVD-VIDEO on DVD disc, AVCHD on DVD disc, or Blu-ray disc format on Blu-ray disc?
Hope all works out well for you.