Mr. Orange killing the woman

Let's be real. If he survived and the cops asked him who killed the woman, he would (should) have probably put the blame on Mr White.

Well that's what I would have done and it didn't look like there were any witnesses...

Just based on what you see in the film, he fired in self defence and quite possibly as a reflex/shock response to having been shot with the gun still pointing at him.

The next bit is conjecture based on that but basically there is a whole world of stuff that favours him not getting into trouble.
1. Self defence, instinctive reflex reaction etc.
2. We don't know if she even had the gun legally, if she didn't then that would add to chances of him not being charged.
3. No witnesses so he doesn't actually have to say anything about anyone else doing it, they just have to prove he did it.
4. The guns are all over the place at the end, tying which gun is his is and doing ballistics and proving he held the gun at that time is more difficult.
5. There may not even be any evidence that the murder happened as part of the robbery, if no witnesses then it might not get tied into it.

ultimately most of what happened next, had he survived, would be based on his own account, without his admission they'd struggle to tie it together enough to charge him.