"Is the plate delicious?"
You don't usually ask if the plate is delicious referring to the actual kitchenware, do you?
Yeah, this is totally awkward. Neither the suggested 요리 nor the "correct" 접시 are correct. Either you would point the thing and ask: 이거 맛있습니까? or specify the name of the dish like: 김치가 맛있습니까?
Absolutely wrong. "the plate" in this sentence should be meant " the dish" or" the meal". We don't eat whole "plate" aren't we?
I have never heard 'plate' used like this. It's either incorrect or archaic.