Going to answer your questions all at once:
@Bib, no the power would not transfer to her. The new decree is not a retroactive thing. So like if a younger brother is already the Lord of his House, and he has an older sister, that sister would not suddenly become the Lord of the House
Also, marriage works a little differently. There are two types of marriages. A Patrilineal Marriage, and a Matrilineal Marriage. Patrilineal means that the wife takes the husbands last name. A Matrilineal Marriage is the opposite, the husband takes the wife's last name.
So let's say Male - Baratheon heir decided to marry Female - Tully heir. The marriage is a Patrilineal Marriage. The female would become a part of house Baratheon.
Now lets do the reverse. Male - Baratheon marries Female - Tully. The male becomes a part of the Tully family.
NOW! Let's try something more interesting. Male - Baratheon (who is the Head of the House) marries a Female - Tully (who is also the Head of a House). It is a Patrilineal Marriage. The Male - Baratheon would become the head of both House Baratheon and House Tully all of a sudden. Because the new wife is not a Tully any longer, she is a Baratheon. Basically forging the two houses in to one single house, House Baratheon. The reverse would also be the case in a Matrilineal Marriage.
@WhatLiesAbove, the Head of the Stark Household could be either the direct child, or grandchild of Sansa. Depending on their age. Aegon is the direct son of Daenery's, but he is in his early 50's.