Hi Oldscruggsfan,
I'm not an expert, but I think it's impossible to post your videos directly on the forum. As far as I know, you need a video hosting website (f.i. YouTube, Vimeo, Instagram etc) to post your vieo, then you post the link of your YouTube (or one of the alternatives) video on your Shameless Self Promotion etc thread. (I think the Seasons uses YouTube exclusively because that's where all the playlists are.)
I didn't have a YouTube channel, and I didn't have the desire to start one, but I did so to join in the Seasons. I used the 'unlisted' setting first, so that fewer people can find it.
You can check if 'oldscruggsfan' or something similar is available as the name for your future channel, or go for a variation on 'ukulele' or Fourstrings or so. Especially if your boss / colleagues or family and friends would not be supportive, you're best not to use the name you go by in real life.
As you may have seen, there are a number of 'headless' Seasonistas, so you could also angle a camera to capture more of your uke and hands, and none of your face. Arcy springs to mind performing as a rabbit (but you'd have to ask more experienced folks how face cams and software with filters or overlays work).
Regarding Public Domain, I find it easier to stick to old songs (pre 1927 this year), traditional songs, some foreign language songs, but even then it can be a gray area. Look at all those covers on YouTube, so you can tell that the vast majority of artists don't mind, as far as you give full credits, and the creators and labels can get some change from the ad revenue. But there are some notorious names you should never cover or you'll be in hot water (run a google search for a recent list of whom and whose songs to avoid).
I wish that other folks chime in with their experience, advice and warnings. I hope to see some of your videos under self promotion or taking part in the Seasons!