I think the clue to the weirdness is when they board Icarus I and the photo of the crew (of Icarus I) that are flashed up is almost exactly the same as the ‘team photo’ of the crew of Icarus II.
To me that says they were all starting to fall apart mentally, like the crew of Icarus I did (I don’t think Pinbacker killed them all, some were in the observation deck when Searle is left alone). Searle was obsessed with what he’d seen in the sun when the filter was low. Kaneda had seen the same thing (what Pinbacker refers to as ‘His God’), and even though he’d finished the repair stayed to see the sun in it’s full glory. Hence Searle shouting ‘WHAT DO YOU SEEEEE?’ at him.
Capa went because he wanted to show he wasn’t just along for the ride. And because Mace volunteered him and he didn’t want to lose face.