It has confirmed that there is no gender in the word prince. But I do think that the Wall won't be standing for much longer. Because there is a lot of theories about what's inside the wall. And the lore behind the Night King is he used to be a member of the night's watch makes me wonder does he know things
Possible. But it seems his main strategy for the moment is to try and go around the wall at east watch since the water could be frozen enough to allow passage. Idk, I am just going off of the hounds vision.