Is the reward for participating in building a mosque credited to the student, or to his father who provides him with the money (allowance)?

If you give charity from the money your father gave you for your expenses and needs, you will receive the full reward for the charity, and your father will receive a similar reward. This is based on the Prophet, peace and blessings be upon him, who said: "If a woman gives food from her husband's house without causing spoilage, she will have her reward, and he will have a similar reward, and the treasurer will have a similar reward. He gets a reward for what he earned, and she gets a reward for what she spent." This is contingent upon that expenditure not causing spoilage to your father's money or imposing an excessive burden on him. Such an act requires the permission of the owner of the money.