Hurr ibn Yazid

This is a thoughtful question that shows reflection on the historical account.

Insofar as there is no answer mentioned in history books, it is not possible to give an answer. 

If I were to guess, perhaps it would have aroused too much suspicion to bring water, or perhaps it was an emotional and sudden moment and he was not thinking about things, or perhaps some other reason.

Ayatollah Motahhari was of the view that it is not correct that they were without water for 3 days and nights. See https://www.al-islam.org/al-tawhid/vol13-no3/ashura-misrepresentations-d...

I don't think there is historical evidence that they were without food, however, the lack of water is much more dire.

God knows best!

There is not much biographical information available about Hurr al-Riyahi (and if someone presents a detailed biography with previously unheard-of information, you should question where they got it from and whether they got it from reliable sources).

This webpage is well-written and explains what is known about the background of Hazrat Hurr as well as the reliability of various reports about him: http://en.wikishia.net/view/Al-Hurr_b._Yazid_al-Riyahi

The webpage does not speculate on his age but given his military rank and position, the respect he was given, the maturity with which he conducted himself, and that he was said to have adult sons (whether or not that report is correct), I would guess that he was somewhere in mid-life, old enough to have passed the younger stages of life but not so old that he was weak or showing signs of aging.