Is it permissible to pay a commission to an accountant from another company in exchange for his dealings with our company, and is this money unlawful (haram) or lawful (halal), assuming a net profit is achieved from this operation?

It is not permissible for an accountant or a representative to take money from those dealing with his company in exchange for his work; because he receives a salary for this work, and taking this money is considered a bribe forbidden by Sharia. The proof of this is the hadith of Ibn Al-Lutbiyyah. It is also not permissible to pay this money to him unless it is the only way to obtain a right or avert harm, in which case the sin is on the receiver, not the giver.