The Princess survived. Everyone who is surprised, say aye.
Ultimately it served as a catharsis/character development moment for most of the characters involved, and the utterly non-romantic relationship between them, but it kept waivering between almost plausible (the CPR/electroshocks in a dispassionate way) to the ridiculous (giving the loaded gun back to the unstable girl). It served enough of a purpose that the entire shower strangle scene wasn't wasted, per say, but the outcome overall was pretty predictable.
So, as a matter of fact, was the result of the Princess Broadcast once they got to the Earth command base- which is to say, nothing. The only people to receive it are the ones in on the conspiracy. About the only interesting note at the base was that it's intended to be a major refugee center and that the government is prepared/expecting the martians to conduct ethnic cleansing, making this base the Last Hope of Terrans.
Slaine got an episode without being beat up and/or tortured, despite having a pistol shot at his balls from close range... and instead got a shiney new mech. the Tharsis, apparently, as part of a 'you're free to do whatever, my debt of honor is repaid' from his current host. Slaine's state seems to be focusing on being disillusioned, but there's no doubt in my mind that he's still going to help the princess.
To finish up, the Conspiracy mastermind is going to drop his landing castle right on Earth HQ in a bid to end the war with a decisive battle. An episode (or three) of combat after our last few 'breather' episodes (pun intended) seem likely, but the result seems predictable at this point: mooks will be massacred, arrogant martians will be beaten by the power of analysis, Slaine will end up arriving to help the princess (but maybe fight with Orange), LT Marito will get back in a cockpit, and the Earth resistance will live on even if the base falls and lots of civilians die.