The scrum master doesn't need to be present during the daily scrum. Neither does the daily scrum need to consist of three questions, which is a commonly chosen format though.

Cross-functional is on team level and not on individual level.

The scrum guide says: "The Product Owner is accountable for maximizing the value of the product resulting from the work of the Scrum Team." The key here is the value maximizing part. Of course, he also comes up with requirements and acts as a go-between between developers and customers, but that is definitely not the best answer here.

The refinement is very important and can take quite some time for that reason, however, it should not endanger the sprint goal.