why not "the children were swimming while it started to rain"?
But try this way and it's accepted : It started to rain while the children were swimming.
But of course, as Sabine said "While" is on "swimming", not on the "rain"
"while" is for actions that last for a while. "to start" lasts just one instant.
the ending "(i)ken is on yüzürmek, not on başlamak
The infinitive is yüzmek
Yuzerken means "while swimmin"' on its own , let me give you some other examples :
Giderken : while going
Bakarken : while looking
That başladı sounds a lot like a başlıdır, like, exactly the same to me as if it had an r. is that normal? will it in real life too?
I don't hear any r and the pronunciation seems fine to me
why is this wrong "the kids were swimming while it started rainning"
This sentence is in two parts, each part with its own verb at the end. Your sentence would be something like 'Yağmur başlarken çocuklar yüzdü.'