Firstly, one of the episodes I've downloaded to my computer has either been somehow moved, deleted, or corrupted, and I cannot for the life of me find any way to download it again through Media Go. Additionally, I did not delete the file, move it, or really do anything with it other than play it once, so I'm not too sure how this could have happened. And no, it wasn't a rental, as a matter of fact purchase was the only choice. Additionally, I've tried to rebuild the library and that did not help either.
Secondly, I purchased two episodes on the Sony Entertainment Network and the only download options seem to involve using a psp, and I only have a ps vita. Is there any way to download this either with my vita or my computer?
All purchased videos in the Playstation Store can only be downloaded one time. It doesn't matter whether it is rented, or purchased to own. You can't download it again, without paying for it again. You can purchase games and video on the Sony Entertainment Network web site, but you can't download the content from the site, even to a PSP. You have to download the purchased content on your console, or Media Go. Any video in the Playstation Store that can be downloaded to a PSP, can also be downloaded to a Vita, but that isn't the problem.