Hello Vil,
"Settle down" in the second example seems to imply "to stop behaving in an excitable fashion".
"Settle down" in the context of marriage is similar; it implies "giving up one's wild ways and creating a stable and orderly family home with one partner".
Birds "settle" on their nests; they "settle down" when, after fluffing up their feathers, they lower themselves onto their eggs.
Best wishes,
MrP




