Translation:What time does the swimming competition begin?
Do you think of the Olympics as a swim meet? Or a competition?
That is very sport dependent to people who have participated in swim meets. While I may know that word, it definitely isn't the first thing that would come to mind.
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Its a meet, olympics or otherwise. Just as tennis is technically a match and not a game
Since the competion is in the future, "will" should be used. "Does" is the present simple tense, but it can be used to reference a series of events that started in the past, such as "What time does the competition usually start?"