What questions should Scrum Master ask in 1-on-1 meetings with developers, PO and stakeholders?

A more fundamental question would be if a Scrum Master should be having (regular) 1-on-1 meetings with anyone.

There may be times when the Scrum Master is teaching, mentoring, or coaching someone on an individual basis, but I wouldn't consider this a 1-on-1 meeting. During regular work, the Scrum Master may have to work together with an individual to help remove impediments, but this also isn't something I'd consider a 1-on-1 meeting.

When starting to work with a new team, it could be helpful to have some time to get to know everyone on the team, individually. In the time of working in the office, this could be getting coffee or having lunch with someone. In the world of remote work, this would more likely be a short video call. The purpose would be to get to know everyone's background, their views on the current state, what they see as problems and impediments as well as opportunities for improvement and find the best ways to communicate and work with everyone. But I wouldn't have these regularly - one or two sessions per person when joining a new team or when someone new joins the team.

What questions should Scrum Master ask in 1-on-1 meetings with developers, PO and stakeholders?

Open questions might be helpful, in order to encourage a train of thought. A Scrum Master seeks to build a consensus view of reality by bringing these people together.

I'm going to flip your question around.  What kind of questions would team members ask a Scrum Master in a 1-on-1 meeting?  If you have a hard time answering that question, then you are starting to understand that 1-on-1 meetings are really helpful as a Scrum Master.  I agree with @Thomas that some discussions early on can help people start to understand each other.  But it should go both ways.  The team member needs to understand the Scrum Master as well.  After that, just the daily interactions will help to strengthen the bonds.

As for the kind of questions to ask, @Ian hit the nail on the head.  Ask questions that will invoke thought.  You aren't telling people how to do things, you are helping them understand what needs to be done and encouraging them to come up with the solutions.

What do you think about the question ¨How are you doing today?¨ and ¨What can I do for you?¨.

Agree with everything shared above.

Will add that 1:1 discussions can become an issue if Team members are bringing to you, what they ought to have courage and openness to bring to the Team. Consider how transparency and inspection may be impacted by having private 1:1 discussions, instead of open discussions as a Team.