Now, Pale Moon is available for Linux. More on this, here.
In addition to the previously mentioned Iceweasel, there's also IceCat, Swiftfox and Swiftweasel.
(If you're feeling adventurous, there's also Conkeror, which is basically Firefox for people who hate using a mouse.)
Flock was discontinued.
Finally, if you want, literally another Firefox installation, you could just download the binary package and install it to another location.
Edit for setting as the definitive answer:
As indicated, the intended browsers should satisfy two conditions: (1) support Firefox addons and plugins, and (2) run separately from Firefox, without interference.
Icecat fully satisfies these demands. More details in this complementary answer.
Swiftweasel also satisfies the demands, but in relation with an outdated version of Firefox.
Seamonkey has a limited support for themes but the most important extensions are supported (more here.)
For details and updates keep an eye on this complementary answer.
Best Answer
The best player I've seen is Miro player. It can play from a lot of sources, torrents, podcasts and feeds. You can browse from thousands of chanels directly from Miro or from their website, so far all popular channels I've seen are there.
Watch their presentation at getmiro.com
You can install it from the ubuntu software center.
good luck!