1. "comes up" in this context means happens or occurs, as in an opportunity presents itself so it's hard not to take advantage of it and claim credit.
2. Not sure, depends on context. I'd guess that if a friend or family member travelled a lot, one could say "I can never keep their trips straight" meaning you don't remember exactly the details about each trip...dates, destinations, duration, etc. To not keep straight means to not remember or to be confused about specifics.