Nice try, but it'll be क्या मैं ही हूँ जिसने नोट किया है कि पानी पिने के बिना ये लड़कियां जीवित हैं?

A native Urdu speaker here, trying to learn Hindi script. Although I am not grammatically inclined, The हैं in the end has nothing to do with negation. It is sometimes dropped with negation but not always. In fact the plural feminine part that हैं depicts can be incorporated with the verb at the end and can be written like लड़कियां पानी नहीं पीतैं. Please note that ैं part on the end of the original sentence depicting nasal H can also be transferred to the verb DRINK पीतैं.... LaRkiyaN paanee naheeN peeteeN. N = nasal shown with a dot (bindi) on the two accented lines over "t". That will have the same meaning without the हैं .

Strict grammar requires the use of हैं, while in spoken hindi, it is often omitted

Yes. Please refer to this link - https://www.duolingo.com/skill/hi/Plurals/tips-and-notes

'लड़का' means 'boy' (singular) and 'लड़के' is the plural of boy, 'boys'.

Both are correct, you may or may or say हैं at the end. It has nothing to do with formal or colloquial settings. You can even incorporate the nasal ending with the verb as I have noted above.

Pithey is only masculine so it can't be used. The plural is only emphasized in the noun. The only part where there can be confusion is when one gender refers to the other.

Doesn't is short for does not and would only be used for singular nouns. For plural it is don't or do not. "These girls doesn't drink water" doesn't sound as smooth and is incorrect English grammar.