Hello!
Cats yawn because they have nothing else to do.
Until doesn't really make sense, so the obvious answer is "because."
Bill arrived late for school when he overslept.
There's no way to arrive to school while sleeping, so "when" fits the best.
The cat crept forward slowly until the mouse ran into his hole.
The goal of the cat was to scare the mouse, so "until" is the best choice.
Lucy was quiet while her little sister was sleeping.
You're trying to describe what Lucy does when her sister is asleep, so "while" is the only one that makes sense.
You clean your room after you have a snack.
I don't see how having a snack would make you want to clean your room, so "after" makes the most sense. Most people eat before they clean, and "because" just doesn't work in this sentence.
I hope I helped!