Is it permissible to pay Zakat at 2.5% on an amount invested in a project that yields a monthly return, or 10% of the monthly profit, or 10% of the total annual profits spent during the year?

If you give money to your friend for investment and stipulate a fixed monthly amount, this is a corrupt Mudarabah (partnership), which must be فسخ (dissolved). You are entitled to your capital along with the profit, and your friend is entitled to a wage similar to his work or a profit similar to his effort. The zakat on your capital is due annually. As for what you receive monthly and spend, there is no zakat on it unless you spend it after a full year has passed.

However, if you give the money for your friend to work with it for a percentage of the profit (if any) and without guaranteeing the capital, then this is a valid, legitimate Mudarabah. The zakat on a valid Mudarabah is due annually on the profit itself, not on your original capital.