Kate Bowman

Still, they had Kate and couple of others in the room with her anyways.  Why didn't they just immediately kill everyone they saw, then?

Further question... since Isaac Newton is the deadliest SOB in space, how does just shutting down the torches prevent the asteroid from continuing on its trajectory towards the planet? Shouldn't redirecting the torches to steer the asteroid away from the planet been a thing?

Balak seems to have been a member of the Batarian Special Intervention Unit, although the game and lore doesn't say - it makes sense since his last rank in ME1 was Commander (wiki) and in ME3 he was an Admiral. Balak had killed pretty much everyone else in the facility. Kate knew that or at minimum suspected that since she lost contact with them... and couldn't re-establish contact even after Shepard fixed the com-link. Balak hated humans. Kate's brother was to be killed regardless. So why would she even give a name? It would make no difference. It might even endanger her own life in addition to her brother's.

Also, when you meet Charn, he says that he thought the operation was going to be a quick slave grab and nothing like this. Balak ordered everyone killed. Aside from Charn, these guys were mercs. Shepard has the choice of letting Charn's group go... or if you're role playing a Mindoir survivor you probably should just kill him and his men because the words "slave grab" would be the wrong answer as well. My last run was Colonist-War Hero so Charn died. There was that, too.

Ironically if you left Balak for the Alliance, regardless of what it said in the Wiki, Balak appears in ME3. Apparently the Alliance did a prisoner exchange.

Always dies in my game, too. Sorry, but "muh culture" isn't okay in taking slaves from people outside of your culture. I don't mean to say it's acceptable even against other batarians but their culture ends when it actively works to steal from me. I wouldn't arrest him. George Lucas: "Greedo shot first." Han would never do that...

Shepard is supposed to take the time to arrest Charn while having to run off after Balak? Was Shepard supposed to hope that Charn would stay put in the meantime? As far as we can tell, the only people who knew what was happening were the people on the asteroid. No was coming anytime soon and wasting time waiting is outright stupid. Shoot him and go rather than waiting to be backstabbed.

I wasn't even going to touch on the Mako. I was talking about time. Shepard was going to have to waste time waiting for people. Yes, I said Alliance but it still plays out the same hanging around rather than hunting down Balak. It's not like Charn was going down without a fight. He had no intention of being taken down. He just wanted to leave and that wasn't an option.

"Shepard can convince Charn to leave the asteroid peacefully, under the promise that Balak will be eliminated and Charn will then be the one calling the shots. In that event, Charn agrees immediately and provides Shepard with a pass to the main facility along with a warning that Balak is a "mean bastard"."

Source: masseffect.fandom.com/wiki/Charn

It may not be an arrest but it also doesn't require killing. I thought this was the case but had to go back to the wiki to make sure.