Is zakat obligatory on money deposited in a bank and a savings account, which belongs to my brother and not to me, and is zakat obligatory on their profits after a full year has passed?

Since your brother lent you a sum of money, it is a debt upon you, and the money in your account is yours. The debt needs to be considered: if you possess other funds exceeding your needs that can be used to cover the debt, then pay the Zakat on this debt if a year has passed over it and it has reached the nisab. If you do not possess other funds to cover the debt, then Zakat is not obligatory upon you for it. As for the profits, their hawl (one year) is tied to their principal, and their Zakat becomes due along with their principal when the hawl is completed.