All I ever knew of these two was their famous duet: "When I'm calling You (oooh hoo hoo, oooh hoo hoo)" and was so turned off I avoided all of their cinematic collaborations. These clips were great. They truly exemplified your point about JM and NE being so much more than stiff operatic purveyors.
Their jousting repartee in the first scene was well written nascent love-making. Incorporating character developing dialogue, believably delivered, into the performance disarmed what might otherwise have played as a forced, absurd serenade.
In the second clip, the "regular" is JM's comic foil. Her skirt skirts the floor! Her cleavage is masked by ruffles. Her gyrations in this context are more scenic exposition than sexual adventure. Though averse to vulgarity, The Production Code was more concerned with message than manners.