Is it permissible for an employee to take the housing allowance designated for family accommodation if the stay is temporary for specific months in the year and not permanent, and is it permissible to take the ticket allowance without traveling?

The ruling on your action of bringing your wife for a period and then sending her back to receive housing allowance and annual tickets depends on the terms of the contract with your employer. If what you do is sufficient for you to be entitled to these allowances without deception or fraud, then there is no blame upon you. However, if there is a trick involved, you must clarify the matter to your employer. If they accept, then there is no blame upon you, otherwise there is, based on the Almighty’s saying: (O you who have believed, fulfill [your] contracts), and the saying of the Prophet, peace and blessings be upon him: "Muslims are bound by their conditions."