No Luffy offered her treasure to compensate the candy that he ate. He then said that he'll take Fishman Island after he defeats her.
Shanks is really questionable to be honest so its difficult to make predictions about him.
Nah I think BM still owns it.
Btw I was thinking that what if Shanks protects Elbaf? He is the only Yonko that doesn't have a major country/island under his name so Elbaf could be the place where Luffy and Shanks reunite.