Nicky

Bad Coop repeating himself reminded me of the last bit of the season 2 finale, Cooper repeats "I need to brush my teeth" twice in a awkward way to Truman and Dr. Hayward before going into the bathroom for the final BOB in the mirror reveal. I think that whatever Bad Cooper is, he can't mimic human behavior very well when exhausted, or maybe it's just that he doesn't know how to act towards people that knew the real Cooper. In regards to the Coopers, I think it might be as you say and thus MIKE saying one of them needs to die is just him wanting Bad Coop punished for tricking the "system" (whatever that might be), alternatively perhaps both of them are weakened by co-existing in the same "reality", which could explain the strange behavior from both of them so far, or be a driving force further on in the series.

I didn't notice this until I looked at the credits just now but yeah, that is the same actor. She's credited as just "American Girl" though and Cooper doesn't really seem to acknowledge that he recognizes her so it might just be a short cameo. Speaking of the credits, Don S. Davis/Major Garland Briggs is credited (with the tag "archive footage" on imdb) in this episode. I thought the face floating by in space as Cooper looks down from the floating platform might be him and it seems like that's the case. He says "Blue Rose" as he floats past by the way.