Is zakat obligatory on the price of a shop that has been sold, and was zakat obligatory on the shop itself before it was sold?

If your brother sells the shop from which he earned his livelihood through rent, then there is no zakat on its price until a full year passes from the day of the sale, provided it reaches the nisab by itself or when combined with other assets. As for the zakat on the shop in the past, it pertains to the income (rent) if it reached the nisab and a full year passed over it. If the income was spent before the year was complete, or if it was less than the nisab, then there is no zakat on it.