I don't like either of them.
When you do the freestyle, how many strokes are there between breaths.
Are these both correct:
1-When you do the freestyle, every how many strokes do you breathe?
2-When you do the freestyle, you breathe every how many strokes?
I think '2' is informal. It does not have the structure of a question.
... I agree that the 'are there' form is safer, but as an erstwhile competitive swimmer (very erstwhile - about 50 years!) I'd expect to hear something that referred to the swimmer's choice (which is what makes freestyle free): 'How many strokes do you leave between breaths'. And even then the verb is questionable: leave, take, make, wait, do, allow...? In informal speech, I certainly wouldn't regard 2 as unacceptable; the question structure of 1 though makes it hard to parse.