Caching.
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It's always caching. https://shouldiblamecaching.com/ That explains why you don't immediately see the newest questions list in its most final version. (If you keep that page open in another tab while you post a new question, you will see a little "(1)" appear which, when you click on it, shows your question as the newest one.)

> Is the question sent to moderator approval first, and then it will appear?

No.

> Sometimes I found a quick edit and quick answer by people above 50k reputation even when the question appears after 2-3 minutes.

Maybe those people were keeping the question list open so that they could immediately spot updates to it?