2) You have mixed up the sexes. It would be very odd if he sat on her laurels. It means that the person doesn't relax even when it appears that he/she has accomplished something. He/she continues to strive for more.
3) The wording is correct. It means that something happened which was probably quite surprising or frightening or shocking but the person in question did not react in any way, he just carried on as if nothing had happened.
If you are looking for just one adjective to replace the idiom, I would go for 1) blunt, 2) not complacent 3) unfazed.
Did you look up all these idioms online, either on Google or in this forum's Idiom guide before you posted the question? Where did you find them?
Student or Learner