What relation do you have to your half brothers brother?

Answer 1

Your half-brother's full brother would also be your half-brother.

Your half-brother's half-brother (assuming he isn't your full brother) is probably what we officially call "no relation," though he might potentially be a stepbrother.

Answer 2

Half-brother or full brother, it doesn't matter. The child of your mother's sibling is your first cousin and the grandchild is your first cousin, once removed.

Answer 3

Technically you are not related at all. There is no blood relationship. Ask them how to address you, aunt is sometimes used.