The basic question is, can the same grill be used for meat and milk. But this question has a few sub-questions/caveats and cases that I'm curious about.
1- I'll assume that the same grill grates cannot be used for both meat and dairy. However, if one were to remove the grates (and any drip-pans etc), and clean the grill thoroughly, could one then use that grill for dairy (pizza for example)? Would one have to wait between the meat and dairy cooking?
2- I'll assume that cooking fish on the same grate as meat, even not at the same time, is not allowed. However, can one cook fish on a separate grate? Would you even need to clean the grill? Would you have to wait in between? Is there a difference if the grill is covered or uncovered?
3- I'll assume that vegetables cooked on the same grate as meat can never be eaten with dairy, even if they were not on the grill at the same moment. However, if one uses separate grates, can one eat the vegetables with dairy?
4- Is there a way of kashering a grill to the point where even the grates do not need to be replaced? For example, could one conceivably leave the grill on for a while, and then immediately use the grill for dairy/fish/food expected to be eaten with dairy?
5- Reverse the questions. Once someone used a grill for pizza, what must be done before using it for meat? Once someone used a grill for fish, what must be done before using it for dairy?
(If relevant, assume all questions are asked relative to generally accepted practice of Orthodox Judaism, please source all answers and note differences between Ashkenazi and Sephardic opinions)