There isn't a word used for "very." 많이 is used to mean "many," as in, having "many years."
I'm wondering this too? Isn't 우리 a sign of respect, and this sentence is otherwise extremely polite?
Sometimes in Korean people refer to family members as our when they are talking to other people, espeacially when they are close to that person whom is they are talking to. Also, some Koreans like to think family don't belong to them. Research this if you are confused. I am not an expert on Korean culture.
Try not to focus too much on the literal translation. But yes. Has a lot of age.