Sentence Diagramming: The bird in the tree sang happily

The prepositional phrase here is describing the type of bird by giving its location. If the sentence were to be phrased "The bird sang happily in the tree", it would be answering the question where as you said. It would then be supporting the verb sang. However, currently, the prepositional phrase is describing the bird, and the question "Where?" is an adverbial answer, and therefore cannot describe the noun bird.

The bird in the tree | sang | happily.

The bird in the tree: subject

sang: verb

happily: adverb

The noun group "the bird in the tree" has the main element bird and as subelements "the" and "in the tree". "in the tree" is a shortened relative clause: the bird (that is ) sitting in the tree.

Unfortunately, your diagram image is not rendering. Given the question posed by the author to whom you refer, I assume you connected the prepositional phrase, "in the tree," to the verb, "sang," rather than to the head of the subject, "the bird."

The way to analyze this, or any other, prepositional phrase is to ask, "What is the phrase telling me?" You are correct to suggest that the phrase tells us about a place; about where. By responding to her with the answer, "Where," I assume you also correctly meant the location of the bird, as opposed to the location of the singing. So, you are 90% of the way home.

The precise and subtle point the author made is that "in the tree" tells us which bird is the subject of the sentence. It does not tell us where a particular bird was.

By contrast, in the sentence, "The bird that was singing was in the tree," the prepositional phrase now tells us where the bird that is the subject of the sentence was.

In my example, the sentence is about a bird that was singing. "That was signing" tells us which bird. The sentence in your example is about a bird that was in a tree. "In a tree" tells us which bird.

It is that sort of contrast that the author is teaching through her question to you.

Can someone water down for me what she is trying to say?

I gather that the speaker is hinting that in the tree is a prepositional modifier that modifies the noun phrase "the bird".

You can also imply a hidden relative clause: The bird that is in the tree sang happily.

The question that would elicit the response is "Which bird sang happily?" The answer is "The bird in the tree sang happily."

{The bird in [that is] in the tree} is a noun phrase and the subject of the sentence.

The question "Where was the bird that sang happily?" would elicit the answer "The bird that sang happily was in the tree."