A. "See him out" means "accompany him to the exit", and this may be because you want to spend as much time with him possible, or because you're being polite, or because you want to ensure that he actually leaves (because his is unwelcome, for example).
B. "Force" would be too strong here. If you force yourself to get into the mood, it means you battle very hard against your natural wishes. Getting in the mood is usually less painful than that: it simply means to do something that will help you get to the point where you really do feel in the mood. In this case the author probably didn't even try, or didn't try very hard.
Student or Learner