Yes, you can say пуста instead of пустая. The meaning is the same.

I did, but it's not accepted.

Not a native speaker, so caveat emptor, but "зачем" refers to the purpose of something while "почему" is about its cause. It's relatively hard to imagine the speaker of this sentence being primarily concerned with the purpose of said plate's emptiness.

I'm native russian speaker. Grammaticaly this phrase is correct. But nobody says like this. It sounds strange.

That "ещё" always goes with an adjective in this case when we want to focus on the fact, that the plate is empty. Actually, if to be honest, that word order you wrote can be used only when you want (VERY RUDELY) ask why your plate is empty, like ‘Why the heck my plate is empty?’ :D But it's hard to explain to a foreigner

Почему еще пустА́ моя тарелка? sounds good. © Cheekyman ;)

I'm going to go with: Because the number of people doing the course who would know that term is small :) Native Russian speakers' reports make the course better for everyone. Thanks.