Is it permissible to undertake a contract from the company at market prices or less, without its knowledge, and without it being part of the employee's job duties, by signing the contract in the name of another person outside the company?

An employee is not permitted to undertake a private project for their employer without the company's knowledge and permission. Deceiving by writing the name of another contractor is forbidden fraud and deception. An employee may undertake the execution of the project if they inform their employer and the employer agrees and contracts with them for the execution; otherwise, no.