Is the agreement with the broker to sell the shop for one hundred and ten, with ten of that going to the broker, Islamically permissible? And is Zakat obligatory on the amount from the sale of the shop, knowing that selling it was only considered a month ago?

There is no objection to agreeing with the broker to take ten percent of the sale price exceeding one hundred. There is no zakat on the price of the shop after it is sold unless its purchase was intended for trade. However, zakat becomes obligatory on it if it reaches the nisab by itself or by combining it with other money, and a full year has passed on it, and its amount is 2.5%.