you are pretty much good on all but the third one. you might say, "after catching him, they charged him with breaking the law."

3) ''The policemen finally caught that guy and charged him.'' - It's redundant to say 'charging him with breaking the law'. If an officer charges you, it's the only thing he COULD charge you with! Can't charge you for NOT breaking the law. If you want to say 'with', you have to say what the crime actually is. e.g. 'charging him with burglary.' 4) ''You should be charged with all this graffiti stuff.'' - Charged FOR, not 'with'. If you want to use 'with' you need to say what the crime is. No need for stuff either. Sound odd.

all of them make sense and seem like something a native speaker would say. the fourth one needs some work, though. I dont think that charge would normally be used in that context. at first glance it looks like you mean charge as in "to run towards someone very quickly" in order to apprehend him. You might say, "after the police caught him, they charged him for the crime."