Is it ok to ask questions in third person omniscient narration? I found myself doing this when my MC was thinking a lot to himself. I thought it helped create a mood of uncertainty or puzzlement. Encyclopedia Brown tried to solve the mystery. He examined the note from Sally Kimball one more time. There was a message there, but what was it? Sally couldn't play the recorder in music class. How was she going to play an advanced brass instrument? What sound does a rusty trombone make anyway? Leroy checked the box 'yes' and passed the note back to Sally. or Encyclopedia Brown tried to solve the mystery. He examined the note from Sally Kimball one more time. There was a message there, but he could not figure it out. Sally couldn't play the recorder in music class. Now she was going to play an advanced brass instrument. A rusty trombone does not sound like it would produce a nice sound. Leroy checked the box 'yes' and passed the note back to Sally.
I've actually avoided posing questions in non-first person PoV for many years now because I thought it was something that just shouldn't be done. I'm starting to cautiously move out of that though and I feel a little daring for doing so. I need to read more so I can see how other authors have dealt with this situation. However, as long as you've already crossed that line of posing a character's thoughts, a question is no different. Looking at your two samples, the first one (with the questions) actually sounds far superior to and more natural than the second. Less words are used for the same effect. The second one sounds... conservative. That may be a personal issue with me, though!
As long as it has context and it's not the narrator asking the question, it should be okay. Your first example is fine. But it always comes down to personal taste and style.