I think some of your premises are mistaken.

>>If I ask 'what is the weather in this city?' >>Does that question make sense without mentioning the city's name either before or after?

Yes, it does, if we're standing in a city when the question is asked. "This" would obviously refer to the city we're in. Likewise, in this instance, "this" obviously refers to the question that is currently being asked.

I'm not saying that 'this' doesn't resolve to anything.

Of course it does. It's like pointing to something and asking 'what's this?'. Of course the act of pointing, or the act of standing in a city resolves 'this' to something else.

But the point is where 'this' resolves to something which has meaning.

A question makes sense, if it is understandable and answerable.

Q1: //TODO

Q2: what's the population of this city ?

Q3: what's the location of this city ?

...

Q22: what's the altitude of this city?

Q23: what's the weather in this city ?

Suppose I ask you "What is the answer to Question 23?".

You'll respond "what is Question 23?" (trying to resolve/concrete 'Q 23').

I'll reply "Question 23 is - 'What's the weather in this city?' ".

You'll respond "well, what does 'this' refer to in Question 23?" (trying to resolve/concrete pronoun 'this')

I'll reply "this refers to the city in Question 22"

You'll respond "well, what is Question 22?' (again trying to resolve/concrete 'Q 23')

I'll reply "Question 22 is - 'What's the weather in this city?' "

You'll respond "well, what does 'this' refer to in Question 22?" (again trying to resolve/concrete pronoun 'this')

So-on, so-forth.. until we reach Question 2, referring to Question 1.

Now, If I define question 1 to be - 'What is the capital of USA?'. Then, by chaining, you can answer Question 23.

But if it do not define question 1, you can't answer Question 23, because I have not given you enough information to resolve pronoun 'this' in 'this city'.

That is the case with OP's question. In order to answer a question, the question must be answerable. In order for a question to be answerable, it must be understandable. In order for a question to be understandable, all pronouns in it must be resolvable to a valid question.

Do you agree that the question 'what is his height?' - is unanswerable IF the asker is not pointing to anyone, or there is no one else in the room, or there is no prior context - because the pronoun 'this' is unresolved ?

I don't agree with that. The pronoun "this" does not appear in the example question you just provided. There's a difference between "this" and "his" and the difference is how they resolve contextually.

And in the OP's question, it's obvious that "this" resolves to the current question that it appears in. It seems like you want to say that this is not obviously the case simply because the question is unanswerable. Yet I'm not convinced that you didn't invent this requirement yourself. Anyone reading the OP's question would clearly understand to what the "this" is referring.

I've given clearer examples in updated answer here - https://math.stackexchange.com/a/3437700/725808

Basically, OP has not provided a base case for his recursive question. As a result, it goes on infinitely, ending up in stackoverflow.

>Because there are still unresolved pronouns in (Q2).

When something is self-referential and resolves to itself, that's the end of the recursive process. There's no need to produce a Q2 that is Q layered inside itself. You go and substitute the entire sentence in place of "this" and form some unresolveable chain of recursion but you do it for no apparent reason. If these were statements in a programming language your expansion might make sense, but not in the context of spoken english language.

I've updated the answer again with hopefully clearer examples.

You're getting stuck because you're used to only 1-level resolution/replacements for pronouns, because that's what we're used to in daily speak.

But I've given a concrete 2-level example, where you will question your own stance of "that's the end of the recursive process", and help you expand the logic to 3-levels deep, 4-levels, 5... to infinity.