Hi again, joshl!
Thank you for the attention you give to this problem!
As I said, I watch local TV stations, and I am afraid that I shouldn't advertise this site's activities, because sometimes they have to remove streams following requests from content owners!
Anyway, when I posted my question I thought there was some simple setting that I had to change; if a special research has to be performed, I'd rather not waste your time!?
The plugins I have installed are standard, they are installed on the other browsers I mentioned; also, the Flash Player works fine on other video sites - YouTube, Vimeo, etc.
As I said, I thought that the message itself - "Manifest is not a valid M3U8..." would be enough to point to the nature of the problem!?