In Verbs^x, Indirect speech^x, Direct questions^x

Yes, you are absolutely right! It is indeed indirect speech (I realized it later after reading more) and then we don't use auxiliary "do" in indirect questions. But I found this to be a tricky one. Yes, I have Swan's book but he doesn't mention that we can use auxiliary do...

If we try and use the same approach: - DIRECT: Why do I have two cars? - INDIRECT: You may wonder why I have two cars . (NOT ... why do I have two cars .)

"Who am I?" is correct if you are asking a direct question. In indirect speech you might say something like "I wonder who I am." Miriam -- ~comes back to edit~ I forgot you asked "why". The verb "to be" doesn't use any auxiliaries in the present simple, so in order to make a...