Is it permissible to trade with another's money, with an agreement on a known percentage of the monthly profits, and to take a percentage thereof as a fee for brokerage?

If the contract between the merchant and the capital owner stipulates a fixed amount or a percentage of the capital for the capital owner, then the contract is void. However, if the contract stipulates a known percentage of the profit for the merchant (as a mudarib) and the rest for the capital owner, then the mudarabah is valid, and it is permissible to agree on paying a monthly amount as an advance, with the final accounting done when the profits are divided.

As for you, according to the majority of scholars, it is not permissible for you to stipulate a share of the profit for yourself. If the capital owner permits the money to be given to another mudarib, then the first agent acts as an agent for the capital owner. If he does not stipulate anything from the profit for himself, it is valid. But if he stipulates something for himself, it is not valid.

Some scholars, however, are of the view that if the first agent stipulates a known share of the profit from the capital owner generally, and then, with the capital owner's permission, enters into a mudarabah with another mudarib for less than his stipulated share, he is entitled to the remaining portion of his share of the profit.