What is the ruling on a government official responsible for government projects participating in a contracting company owned by his brother-in-law, receiving a percentage of the profits in exchange for helping the company directly obtain government projects? And is this considered a bribe?

If your son-in-law's employer stipulates that he should not engage in private business, then he must adhere to that condition and not partner with you. Circumventing the system is not permissible.

Even if the system allows him to participate, it is not permissible for him to award projects to your company, as this is akin to an agent buying from himself, which is not permissible.

The person responsible for projects must consider the general interest of the work, and it is not permissible for him to exploit his position for favoritism. Furthermore, it is even more impermissible to give him anything in exchange for awarding projects, as that falls under the category of prohibited bribery.