in what ways does inspector goole carry out an inspection of all the characters in what happened to eva smith?

I can't write your essay for you but I can comment on the inspector. Priestley describes him as speaking "carefully, weightily ... and [he] has a disconcerting habit of looking hard at the person he addresses before he speaks." He initially seems to be an ordinary Brumley police inspector, but (as his name might suggest) comes to seem something more ominous--perhaps even a supernatural being. The precise nature of his character is left ambiguous by Priestley, and it can be interpreted in various ways.