Is it permissible for an employee to take payment for repairing devices belonging to the employer or their family, if the employee performs the repair themselves outside of working hours and tells the employer that they sent the devices to a repair shop?

If your employer, or his wife, or his child, or others, commissions you to give a device to someone else to repair it for a fee, then you are not allowed to repair it yourself and tell them that you gave it to someone else. Similarly, it is not permissible for you to do so if they give you the device to repair it yourself without a fee, on the basis that you are volunteering to do so. However, if they give you the device to repair it yourself for a fee, then there is no blame upon you for demanding the agreed-upon fee between you, or a customary fee if the fee was unknown.