Photoshop is a Photo editor, Premiere a Video editor. There is nothing called "photoshop premiere elements" except as the title of both products on a package.
About the only overlap is you can create titles, graphics etc. and import them into your videos or use Photoshop to further correct/enhance a still grab made from a video frame since Premiere's tools are weak in that area. You can already do that with the Photoshop Elements you own.
I personally use Photoshop for my still work and although I do own an earlier version of the Creative Suite, I much prefer the interface on
Sony's Vegas Movie Studio Platinum - over the included full version of Premiere in my Creative Suite pkg.
Poke around on the websites, most of the video editors have a free trrial you can download/install - often they're time/file size limited or embed a watermark in your finished product till you purchase the product key but it allows you to explore the design/features.
I used the full Premiere years ago in a past job, I still like VSMP better. Either product has an upgrade also, Premiere Elements to Premiere or VMSP to Vegas Pro which does more than I need so I've never upgraded.
I don't know because I don't use it but I thought Lightroom was only for
photo manipulation also?