The verb generally agrees with the subject. There are times when the verb "to be" can agree with the complement, as in the sentence "There are five people waiting for you", and this may be where confusion sets in. However, the phrase "on the plates" is neither a subject nor a complement, but a prepositional phrase which gives you extra information to help you understand what exactly is being asked.
"What" is the subject here, and this is what the verb tends to agree with; and "what" is, grammatically, singular.
In a sentence like "What were they doing?" the situation is different: "what" is an object, so the verb doesn't agree with it; instead, it agrees with "they", which is the subject.
As for recommending a book, the stock-in-trade is English Grammar in Use by Raymond Murphy, which is available in several versions for different levels of English. It's a reference book with exercises, though, and not an actual course book.
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