I know that か is the 'question marker particle', and can use it confidently in formal sentences.

However, when it comes to casual speech and very short sentences, what is it's usage?

For example, if you wanted to ask 'Why?' - 'なぜ' - leaving the subject of the sentence assumed - would you need to add 'か' at the end to mark that it's a question, or is an intonation in pitch enough?

Or, say, you're communing in Japanese and you don't know the meaning of a word spoken - 'みず', for example. Would repeating the word as if it were a question, without adding 'か' be correct?

TL;DR can you ask short questions without using 'か' if it can be assumed that the word is a question anyway?

If 'か' IS needed in these circumstances, please specify if it's an issue of being correct or being polite.

Thanks!