Is it permissible to open an agency for an application that includes both permissible (halal) and forbidden (haram) videos, in exchange for a percentage of the profits?

As long as the application contains both permissible and impermissible content and it is not possible to control it, it is advisable to refrain from opening an agency for it. It must be abandoned if the viewing of impermissible content is predominant among its users, because the ruling is based on what is predominant. Al-Shawkani forbade the sale of anything whose benefit is exclusively in something impermissible, or whose predominant use is in something impermissible, or whose intended use is for something impermissible.