Back to math.
There is something very odd about the trial. For one thing, Superman's deduction about the planet still being there should have been obvious to everyone. For another it seems unlikely that John's ring should have the power needed to destroy a roughly earth-sized (I'm basing this on a stated population of 3 billion) planet, let alone that he could have done it with a blast that was only meant to disable a small spaceship.
Hawkgirl vs the Lanterns. When Hawkgirl goes after the bestial-looking Lantern (he isn't names but looks like Arkkis Chummuck from the comics) his ring aura protects him from her mace but she is able to knock him down with 3 blows. Hawkgirl embarrasses four of the Lanterns in the fistfight that follows. The lanterns involved appear to be Arkkis Chummuck, Galius Zed, Tomar Re (or Tomar Tu), and Larvox. I cannot find anything about any of them having special physiological advantages or hand to hand training. It's hard to say whether the fight is meant to convey that she has mild super strength or that she has human level strength and is just very skilled. Several of her actions, like lifting Larvox over her head and throwing him, and sending Galius Zed bouncing around the room like a ball suggest that she may be somewhat stronger than an athletic earthwoman of her size.
(On a side-note, I hope that the orange-skinned Lantern is Tomar Tu and not Tomar Re. Tomar Re has a long and impressive back story and it would be a shame is he was such an ass.)
Kanjar Ro's ship's blasters momentarily stun J'onn and Superman. He also uses 4 blasts to bring down a small landslide on them. based on this, I would say that the blasters don't appear to be any more powerful than conventional air to air missiles. Kanjar Ro's ship withstands half a dozen blaster hits from the fighter Hawkgirl is using without visible damage but Superman flies completely through the body of the ship showing he can hit with much greater power than the blasts, unfortunately there is no good way to measure the power of this feat.
Superman breaks through the execution dome with a single punch. This appears to be about 4" of metal plate. It's in line with his work on the much thicker door in Episode 1:2.
GL brings the League and the Guardians of the Universe to Oa in an energy sphere but the method is not explained. Flash has another poor showing on Oa. He takes out two Manhunters, but skids to a stop when confronted by three more and looks like he's in trouble when GL rescues him. A little later he's racing up a wall dodging a barrage of fire when a stray piece of shrapnel hits him in the head. The best explanation I can think of for Flash's performance in the series is that his mind can's work fast enough to keep up with his body.
The Manhunters turn a big gun on the Leaguers and John shields them with an energy dome. The blast melts through an curcular area about 120' across and we see that it has cut through at least 5 decks at least 2' thick each. That's something like 19000 cubic meters, which (if we're talking about steel) would weigh 149000 metric tons. It takes 1,964,500 Joules/kg to vaporize steel so the blast is 293300 gigajoules or the equivalent of 70.1 kilotons of TNT. IMO it's John's most impressive feat in the series.
BTW, this weapon may be roughly as powerful as the Watchtower's energy cannon. That was said to have the power of "a small nuke" and the Manhunter cannon is about 4.4 times as powerful as the Hiroshima bomb.
Note to self: Try to figure out the energy needed for Hawkgirl's mace to snap off that big @$$ cannon barrel.