Is a responsible employee's request for a percentage of a project's profits from a company in exchange for his facilitations and efforts considered a forbidden bribe, and is it permissible for the executing company to accept this offer under duress?

If what the responsible employee will do is part of his job, then it is not permissible for him to take money from your friend, because that is considered bribery and forbidden gifts, and it is not permissible for your friend to give him anything. However, if he works in another department that has no relation to projects, then it is permissible for him to act as an intermediary for money, provided that he does not have a role in preferring your friend over someone better, or informing him of confidential information about bids. Bribery is one of the major sins that Islam has forbidden, and "the Messenger of Allah, peace and blessings be upon him, cursed the briber and the bribed." So, if the work of the responsible person is forbidden, then the work of the intermediary is also forbidden.