Umm... I don't think there are any public domain viral videos. Unless the creator said they were releasing it to the public domain it automatically is copyrighted.
If the work is truly public domain, then you have nothing to worry about. You can download and upload a full public domain movie because well... it's public domain.
regarding your question about editing - I recommend using Adobe products to do almost everything (even though I don't use it for video editing) because you will be able to work with people who use Windows and Mac and because I feel adobe products are the most "industry standard" for video editing and special effects (minus maybe Avid if you are in the TV world)
if you never edited before, I would suggest using either a free trail or getting a free program like iMovie (I've only used it once about 11 years ago)