1) In the first clip, it appears Rose Marie does not believe Mountie Sergeant Bruce is sincere with what he is saying via his song. She even made fun of his singing. In the second clip, she seemed like a fish out of water (so to speak). Then, Rose Marie saw Mountie Sergeant Bruce with those two women. I think she would have rather of been sitting with him, than singing. By the end of the song, Rose Marie seemed embarrassed. I think Mountie Sergeant Bruce felt bad for her.
2) I have heard of Nelson Eddy and Jeanette MacDonald. I am not familiar with their work (yet).
3) I would say that male/female relationships were complicated back then (and still are today).