Near the end, it says the the players manage to destroy the Dark Window, Aeterperax automatically knows and will likely just murder Rima if they take too long. How exactly should the DM arbitrate this? I'm thinking maybe if they take longer than a few days, Aeterperax should use a whispering wind scroll (he doesn't have them by default, but the DM can obviously give him one) to say something like "Come face me, cowards! Or the girl dies" along with a description of where his lair is (this might take more than one scroll). If they take more than, say, 4 hours, she'll already be dead when they get there.
Depends on the game, I think. In most games, I'd have Rima's demise just sort of hanging over the party to motivate them to move forward. She'd only die if the PCs did something in the fight with Aeterperax to endanger her.
In a game where I'm more interested in something grittier, I'd go with if the PCs find him in less than a day (allowing for a single rest essentially) then she'll still be alive. Any longer and she's dead.