Icarus I's distress signal

Pinbacker's desire is to stop all efforts to save the sun. He used the distress signal to distract the Icarus II team from their mission and potentially destroy them himself as well.

The assumption is that he killed the crew, because he was crazy.

Crazy people do crazy things. There's no reason that statement shouldn't include set off distress beacons.

That said, given the total control the computer APPEARS to have over the ships core functions, and its ability to detect life forms and calculate expiration due times depending on oxygen levels etc... Isn't it just possible that the computer detected the sudden loss of crew life signs on board, and turned on the beacon itself, without input from Pinbacker?

He was crazy, but I do not think he urdered the whole of the crew.
We see three silhouettes sitting peacefully in the room, burned to death. So either he killed them and arranged them (what for???), or killed them while they were sitting there (although then they would probably be in different poses). Or more likely, they all webt a bit crazy. Maybe he went mad after the crew went funny.

I think it's also likely that the whole mission started going down, like they all suffered hallucinations and what not, but before commiting suicde by being burned by the Sun, someone set off that distress signal.

In the beginning there was nothing, and it exploded.

he set it himself, as bait

The Icarus distress signal just sounded so cool, that's why the commander had switched it on. Here's 10 minutes of the distress signel:
https://www.youtube.com/watch?v=N-r4pPrHarw

It was later reused in The Thing (2011).