2nd Hazoret's Undying Fury in a turn will NOT empty mana from spells fetched by a 1st HUF.

Magic: The Gathering - Puzzle Quest MtGPQ Bugs & Technical Issues
1

In my hand i had 2 HUF in hand, 1 fully charged.

When i cast the first HUF, it fetchs 4 Deploy the Gatewatch and casts 2 of them.
Deploying creatures, Zacama, Primal Calamity triggers multiple cascades filling up my 2nd HUF.

I’m prompted to cast the 2nd HUF while i still have 2 Deploy the Gatewatch with full mana waiting to be cast.
The 2nd HUF resolves and fetches 2 more Deploy the Gatewatch, but does not empty mana from the previously fetched Deploy the Gatewatch.

All the remaining Deploy the Gatewatch continue to put creatures into play until my hand is empty.

2

It shouldn’t. {{pageTitle}} | mtgpq.info - "You fetch the first 4 spells in your library, reduce their cost to 0, then each card in your hand is fully drained of its mana. This spell cannot fetch other copies of itself."

It doesn’t give them mana, instead it reduces the cost to 0. So if you drain the mana of a card with 0 cost, it will still cast as intended.