If I ask my children or friends ' why did you do that? ' I will say どうして、そんなことをしたの？ どうして、そんなことをしたんですか？ どうしてis more colloquial and softer.

なぜ and どうして are the same meanings. Native speakers don't usually use なぜ in conversation, that is usually used as a written langage, or in speech people use 'なぜかというと’ , I think. I often hear なぜ used by non native speaker, it's not incorrect, but どうして or なんで are more natural in conversation.

it's better to use なぜ because it's formal than どうして . when you say どうして your partner may think that has done wrong or bad job. good luck!

I'm not a native Japanese-speaker, but I'm my notes I have this: なんで -> very informal どうして -> informal なぜ -> polite