Is it permissible to invest surplus orphan funds in projects that may be subject to loss, and is it permissible for the director of the organization to take a percentage of the profits from this investment?

The agent representing the donors for orphans disposes of the donation funds according to the donors' conditions. If they authorize the association's administrators to oversee the funds, then the administrators may act in a way that is most beneficial for the orphans, such as investing surplus funds after due diligence and consultation. They are not liable for losses if they have not been negligent. As for the questioner taking from the profits, as long as he is well-off, he should not take anything for himself unless the judge or the donors stipulate something for him, in accordance with Allah Almighty's saying: (And let him who is rich abstain [from taking wages]; and whoever is poor - let him [then] take of it in a just and reasonable manner).