。
She asked everyone the same question, one after another.
Literal
[topic-は] everyone [to-に] in-order same question [object-を] did.
順番に ('in order, one by one') is an adverb formed from 順番 ('order, sequence') + に, marking the manner of the action — going down a sequence of people. 質問する ('to ask a question') is itself a Sino-Japanese verb; the alternative 質問をする (with を) breaks 質問 out as a separate noun, here written as 質問をした for that effect. みんなに ('to everyone') marks the recipients with the addressee に. The mental image: a teacher or interviewer methodically going down the line, asking the same thing to each person.