This is tricky because the phrase "X the hell out of Y" belongs to colloquial and informal English, not to standard English. Grammatically, all of your phrases are correct. However, none of them make good sense and none of them are "idiomatic"--they are not something a native speaker would say. The problem with the third one is that you don't "cook a pan," you "cook food." You cook something you are going to eat. You can't eat a pan. The food might be in a pan, but you don't cook the pan, you cook the food. So, if she is frying chicken in a frying pan, you could say "She cooked the hell out of that chicken," but not "She cooked the hell out of that pan." The phrase "X the hell out of Y" indicates that the speaker is surprised by something extreme. "Hell" is close to being a bad word. (A hundred years ago it was a bad word). Using "hell" gives the feeling that the speaker is experiencing strong emotion, and has slightly lost control of their language--or wants to go a little outside the bounds, in order to express that feeling. It could be expressing criticism--"She really cooked the hell out of that chicken, it was all dry and slightly burned," "get the hell out of my way." It could be expressing approval: "You cooked one hell of a fine chicken."

Hi Boom, "the hell out" is simply slang for "to an extreme". So, if she only hurt you a little, no. If he cut the tree down professionally and efficiently, no. Do you see where I am going? There are also many other ways to express that he cut the hell out of the tree. "He really butchered that tree". "He cut that tree until there was nothing left to it". "She hurt me like I've hardly ever felt before." "she hurt me like she mean to!" I hope this helps, Stephen

these things have to be used in the correct way, so don't try to use them until you really understand them. 'she hurt the hell out of me is very strange, nobody would say that. and the pan? but, she didn't cook the pan!