All right. So, pretty much the only reason I got Limeware was because this website, WatchThisFree.com, said that if I did get it, I could download any video on their website (I am, in fact, only interested in one video on the website).
My question is: How would I go about doing that?
The website gave me the link that allowed me to download limewire (Version 5.3.6). But I don't know how to get the videos on the website onto limewire. Whenever I click the link on the website, it says my security settings won't let me download the link, so that's out.

It sounds like a torrent file. You would download the torrent file (.tor) file. Then open that with LW which would attempt to download the actual torrent file content.

I'm not sure why they linked you to LW 5.3.6, that is an older version. LW 5.5.10 is the most recent version. And I certainly hope you did not pay for this!!! If you did, you were most likely scammed.

As for why you cannot download the .tor file, chances are it's your security software not allowing you to. You would need to allow .torrent files (.tor) to be downloaded via your browser settings & your security settings.

Cosi.2010.DVDRip.XviD.avi

That's the name of the file. And the only download button there is says "DOWNLOAD: Fast Sever Limeware".

Send me a personal message with the URL Weblink & I will have a look at it & see what trick there is.