It seems unclear who (or if anyone) shot something at Church, and if why. But clearly before that, even if very shortly before, at some time he'd "armored up". Whatever else, he's knocking Alice about, and she hopefully has a way to stop or reverse her motion. We don't know how she started moving, but Church was able to counter her (and then some) with a lot of force and without moving backwards himself. So we'd imagine all three of them have some way to counter near zero G. If it's just Church that might be a very bad thing, at least for the others.
So Gavia is shielding/hiding/helping/moving them, Sedna is far more protective of Ardent than she is "capturing" anyone, and Pate is still out of his element.
Church seems far more reactionary to the immediate threat than to what else happens later; attacked, he counters. Does that mean anything for later? It's entirely possible the people in charge of this place intervene. If not, who knows. As far as capturing Pate and using him as leverage, it's entirely possible that it's been prearranged that he's expendable. Or Church isn't quite as loyal in reality as he's been carrying on. That is, why would a seemingly pretty much immortal indestructible being would throw in their lot with a low-tech criminal mastermind crime boss (or what have you) sort of short-lived human anyway. Life debt seems unlikely bordering impossible, how could he be coerced, what sort of romantic entanglements would be at all enticing, economics seem to have no bearing, and so on. Political or visionary perhaps, but then one questions the motives there to carry it out, that content is at least a bit questionable given the violence and coercion used to get to space for a chitchat with some trees or whatever they are.
Not that we have any indication that there are any such plans or ever have been, but I wouldn't trust in the success of any plans using Pate's physicality as a bargaining chip. Not that it wouldn't work if things are as they seem, but at the least Church seems unconcerned of such. Although maybe it's just because he thinks he doesn't have to worry about it, or if he does he can just get his revenge on everyone after if it goes wrong.