I hope you get my point, because i think my english is not the best (but I'm trying)
In my opinion the words "warum, weshalb, weswegen" have slightly different meanings.
Q: Warum stellst du diese Frage? (Why do you ask this question?)
R: Weil mich die Antwort interessiert. (Because I'm interested in your answer.)
Q: Warum weint das Baby? (Why does the baby cry?)
R: Weil es Hunger hat. (Because it is hungry)
In both cases you ask for "Grund (reason) oder Motiv (motif)" for a fact.
Q: Weswegen stellt du diese Frage? (What's the reason for your question?)
R: Weil ich mich mit dir unterhalten möchte. (Because I want to talk to you)
Q: Weswegen weint das Baby? (What's the reason for the baby crying?)
R: Weil es die Mutter aufmerksam machen will. (Because his mother should pay attention)
Here you are asking for a "Zweck (purpose)".
Darum/Deshalb/Deswegen are synonyms, they developed in different ages and different places, you can use them how you like it.
Your example "Mich interessiert die Antwort, weshalb ich diese Frage stelle." is not a direct question (always with a question mark), it's an indirect question including the answer. So I would say, it's no question, it's an statement.
I hope this helps.