A:Answer The answer here is a qualified 'no'. This is not Adobe Acrobat, so you can neither completely manage nor completely edit pdf files in that manner.
That said, Photoshop Elements supports importing pdf files, and you can also save PE creations in pdf format. I have (many, many times) downloaded registration form pdfs, imported the pdf into Photoshop/Elements, added a transparent layer 'over' the form, used the PE Text Tool to complete the form on the new layer, and then either saved the now-completed-form as an email-ready pdf, or just printed it, thus converting my computer/printer into an expensive typewriter.
But the newly-saved pdf is just an image saved in pdf format. You could conceivably import a pdf into PE (which, to my mind, converts it to an image), cut up and redesign the image, and then save that image as a basic pdf. But I suspect many (if not all) Acrobat-exclusive traits of the initial pdf would be lost.
This also highlights one of the underrated uses of Photoshop and Elements: the capacity to import and export such a large variety of file types. Photoshop owners often take its role as an 'file translator' for granted.