Is this essay to get a navel piercing convincing? (parents please respond)?

As far as essays go, I think it's probably the most convinging one you'll come up with. There were a few grammatical errors, but you did your research and did your best to let your mom know that you're a responsible human being. That's what counts. If she says that you can have a belly on piercing, then you need to make sure you live up to your word. If she says no, then be mature about it. Don't throw a tantrum or get an attitude because it will only convince her more that she shouldn't let you have one.