I wouldn't say that there is a question that only my religion answered. But rather I would say that there are a set of beliefs that are found only in Islam.
For example, God is One, why do we suffer, what happens when we die, purpose of life,free will ....
These things that I mentioned are explained differently by every religion, but only one answer is the true answer.
I can't give you a definitive answer to your question. But I can tell you that from scratch, I would begin with the religion that teaches that there is One God because I am sure of that. Second, I am sure that God didn't send us to this world to live by our own desires so I am sure that there is something for me to find out. Third, that religion has to have something that proves it and talks about it, something that you can someone can find and be able to understand the religion through it, something like a book.
I would say that these three questions can lead me to what I am looking for. Of course, if you ask another muslim, he will have a complete different list of questions and approaches.
A right religion should have answers to all the question THAT NEED AN ANSWER TOO. so I would suggest instead of asking me what are the questions that my religion had answers to, you should start your own list of questions and approaches.