You can say a few things to the mercenaries.

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You'll end up fighting them regardless. The vorcha in front should die fast. The problem is that the krogan know to hang back and hide when they get hit. This means it's a pain to actually kill one. Just try to hit one or two with a series of abilities to bring them down. Once Kureck loses a few krogan, he'll tell the rest to just charge. Now that they're out in the open, gun them down. Kureck will rush after that, so take him out too.
Just one door left, so go in and find Aresh in Jack's old room. He apparently wants to rebuild the whole thing. Naturally this is bad. Jack's going to blow up the base regardless, so that isn't the problem. You just have to decide what you want to do with Aresh. You'll need to do a paragon interrupt and a paragon speech option to convince Jack that killing Aresh will just finish the corruption that the place had on her. Renegade can convince her that killing Aresh will clear her mind.
Once you've made your choice, you can stay behind to look at Jack's room. You can look at the bed, the desk, and the blood stain in the wall to learn about her escape. Then you just have to hold "F" to escape and watch the base explode.