Learn English – Is “I just might have a chance” grammatically correct

1. Your understanding of the sentence is correct—it means that Harry's room is the one on the right.

2. It is grammatically acceptable, but a sentence that is grammatically correct is not necessarily meaningful. In this case, however, it is understandable, but your phrasing of the sentence would be the complete form.

3. Personally, I would not use this construction; it's a rather unusual one. Using this sentence might imply familiarity or distraction, depending on the observer.

4. I can think of several, but they are not in the same style as your quote. Most sentence of this type, such as You are my doll, use meanings that have become embedded in the language and are reported on in dictionaries. Sentences like those in your quote are extremely unlikely to be encountered and I would not recommend using them.

Your reasoning (You cannot treat "both of us" as a list of two alternatives because 'both of' explicitly means they are not alternatives) is correct.

There is no syntactical explanation. "One of (the) both of us" is as grammatically sound as "Colourless green ideas sleep furiously". It is the semantic content of the words that makes both them unacceptable.