What is the ruling on shooting and hunting games and intelligence games that rely on concentration without cheating, and is it permissible to open a place for them for a fee, and to offer prizes to winners while they pay for playing?

If games are permissible, beneficial, and develop intelligence, it is permissible to charge a fee for them. It is also permissible to offer prizes to winners as an encouragement, but not from the players themselves. However, it is more prudent to refrain from this to block the means to gambling and to safeguard one's religion.