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!
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grammar questions
Usage of 'か' in short sentences
## The OP is looking for options in **" Casual speech"**

In the spoken language you don't need 「か」.

With this you make a rise in intonation at the end of the sentence to indicate
that it is a question.  
All of these examples below translate as "Do you want this?"

> これを欲{ほ}しい？

This can also be used:

> これを欲{ほ}しいの？

Of course someone just learning would be better to stick to using the polite
form such as this:

> これを欲{ほ}しいんですか？

Using something like the below example can come across as being rather rude if
not said correctly. Sticking to using 「ですか」 should be your goal until you know
how to properly use it in a sentence.

> これを欲{ほ}しいか？

So your example would be fine to say something like this:

> 彼がいつもあそこに立っているのは **なぜ** ？
>
> Why does he always stand over there?
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answer