Is paying a sum of money to a police officer in exchange for bringing cases of detainees considered a bribe, and does the same ruling apply to a non-police officer?

There is no religious impediment for a lawyer to seek assistance from individuals (including a police officer outside his working hours) to guide clients to him in exchange for an agreed-upon fee. This falls under the permissible category of brokerage, as evidenced by the Almighty's saying: "And for him who brings it is the load of a camel, and I guarantee it." This is provided that the conditions for representing detainees are observed.