The cute and somewhat Roddenberrian thing about "Coming of Age" is that when Remmick drops the Internal Affairs act and says that he'd consider it a privilege to serve on the Enterprise, it very much looks as if our heroes would actually welcome him there. Sure, Picard at first gives the stereotypical icy silence combined with The Look (TM), but he gets over it, and in the very next sentence says he's not holding the events against Remmick.
I'm sure Picard also appreciated that Remmick performed his duties well. Internal Affairs is antagonistic by nature, and if Remmick made people uncomfortable by conducting his investigation, he was doing his job exactly as he was supposed to, something that wouldn't be lost on Picard.
Exactly. Remmick was doing his duty, and nobody can fault him for that. If he spoke like a jackass to the crew, it was because he was supposed to. IA-type people always are like that, because they have to be.
As for Remmick's death in "Conspiracy": He was already dead. Remmick died as soon as he was taken over by the mother creature. What died in the episode was not Remmick.