Yes, there is a checkbox in the bottom left area of your UV window: select "by element" which will select the whole UV island. There are also buttons right next to that to grow or shrink UV selections & pick UV rings or loops.
The rings on the tail should be much more subtle and closer together. The incisors should also be flatter and closer together - they're used mostly for gnawing rather than puncturing. Look at the one on the right in the concept image above.
He'll be a little tricky to fit in without things getting silly, but lord knows if Marvel can pull of an Avengers movie without the ridiculous concept coming apart at the seams, the chap with the magic rings shouldn't be that difficult to ground.
You can extrude the ring of inner edges in on XY and with all of them still selected merge edges to center Also, you can set materials in unreal to be two sides, so you won't have that issue.
I did, actually; I tried scaling the larger ring so that it was about 3 or 4 times larger; it ended up with the same effect. It's not being resolution-bound, because the pixels are of the wrong color, not just a blur.
Here's the boxing ring I made which the robots fight in. Jati made the mist effect. And here's the robot that I modeled. He is meant to be smaller, sleeker, and faster than the other bots. This turnaround was rendered in Renderman.
You're using roughly a third of your polygon budget on the hands & pendulum; a simple alpha masked quad would work well for the hands. The clock face is really unnecessary - the normal map will show the rings without the cost.
You don't need the edges marked with red. I assume you forgot to delete them before you duplicated the teeth. You can collapse the edge rings marked in blue if you want to save polycount.
The easiest way I've seen this done is with a simple sphere and animated UV's. You can do this in Unreal using a panner node in the material shader. You can also add other effects like the mud rings.
Very cute, reminds me a bit of some of the candles and things my mother had around the house. The eyes look a little off with the puckered ring around them, but I don't have a suggestion for that right now.