What is the ruling on taking money as a loan or a gift from a person who professionally teaches the game of bridge and earns through it?

If the game is free from the prohibitions mentioned in Fatwa no. 30937, then it is permissible, and learning and teaching it are permissible, and taking a fee for it is permissible. However, if it is accompanied by prohibitions, then it is not permissible to practice it or to teach it to someone who will practice it in a forbidden manner. Therefore, your brother's fee for teaching the game is lawful if it is free from prohibitions.

Regarding competitions, if they are in archery, horse racing, or camel racing, it is permissible to take a prize for them, subject to their conditions, as the Prophet, peace and blessings be upon him, said: "There is no prize except in archery, or hoof, or paw (camel or horse)." Anything other than that, it is not permissible to take a prize for it. You should assess your brother's earnings based on what has been mentioned to determine their ruling.