Which plan are you on? What you can do might be different for Sprout compared to the other plans.

You cannot delete priority as there is functionality attached to it. But you can choose whether it is visible to customers or not. State and category are not standard fields as far as I am aware (we don't have them). So I assume you can remove them. 

Apart from status, agent and group only requester, subject, description, and type are default and cannot be removed. But then I would have assumed you need all these fields. For all fields you can choose if the customer can see them or not.