Tae Rabel
Premiere Elements 13 has the potential for creating a variety of effects including the ones shown in the wedding video either by using the many effects and adjusts and a combination there of. As for the cloud effect, that could be produced by using cloud brushes in Photoshop Elements to create clouds on a transparent background (psd or png save) and then importing that cloud file into the Premiere Elements project.
I do not believe that the answer is Elements vs a Pro version. I believe success will follow depending on your knowledge of the program and how skilled you are in using the tools.
Have you had any experience using Premiere Elements? If you have not, but have a lot of experience in video editing, you might want to download and install the free 30 day tryout of Premiere Elements 13 and see if it will work for you to create the effects you want. Focus on the fx Effects including presets and Adjust items.
Please check out the Adobe Effects Reference document
Adobe Premiere Elements 11 * Effects reference
Please do not hesitate to ask if you have questions or need clarification.
Thanks.
ATR