As far as it failing to download from the sites that you do want, could you please send us a log file so that we can seen what is happening in the program? You can find it Jaksta by going to Preferences > General > Find Log File.
With the automatic downloads from YT and FB, unfortunately there is no way around this at the moment. The whole point of Jaksta is to automatically detect streams and download them and there is no ability to filter out specific sites.
To be honest, I'm surprised you haven't had this problem before as it has always been the function of Jaksta to detect and grab streams indiscriminately.
The next version we release, which should be in the next several weeks, will feature a URL downloader bar were you enter the link into Jaksta and it downloads it without the need for the stream to be active. This is the only alternative that I can suggest, as you could turn the automatic detection and download off and then just enter the URLs of the videos that you do want, and continue to browse FB and YT without any problems. Hopefully the update will also fix the problems you are having with those sites that you are interested in, if we cannot fix it in the meantime.
This update will be to V2.0 and it will be a paid upgrade, but it will be offered at a discounted upgrade price to existing users of Version 1.X. You should receive a notification when it is released.
I primarily use Jaksta for cam4/chaturbate and used to be able to browse other sites like Facebook or watch Youtube vids at the same time without Jaksta pouncing on those sites too. Now I've upgraded my OSX to Yosemite (from Lion) and Jaksta to v1.5.1 and not only is it not recording what I want it to (Chaturbate), it IS ripping all kinds of trash files off of nearly any other site I open including Facebook and Youtube (I don't want it to download Youtube vids...there are other ways of doing that if I need a YT vid). Is there a way to filter out Youtube/Facebook media so that I can browse those sites without Jaksta ripping anything and everything off the pages?? This program used to work so well for me.