Could you say "Anh ấy bơi khi nào minh muốn" to avoid repetition?
Yes. Alternatively, you could use "anh" alone after having already used "anh ấy."
Is it me or does the speaker say bưi instead of bơi. I am dumb?
Try listening to how to pronounce "ơ" alone. Maybe that will help. Also, listen with your eyes closed.