Ok, I got an e-mail from Tim Uren with the official clarification on how Zhar's ability works. I'll post this on the BGG and in the Official Answer thread so that it remains visible
Thanks for the question! The short answer is Zhar's ability does interrupt the steps of resolving a mythos card. Finish resolving the card once the ability stops adding more mythos cards.
To address some of the specifics, when investigators must open a gate, the doom track advances and then the gate opens. At that point, before a monster appears, roll the two dice for Zhar's ability. If doubles are rolled, start resolving another mythos card. If investigators must open a gate while resolving this card, the doom track advances, the gate opens, and then roll 2 dice for Zhar's ability again. Once you resolve a mythos card without Zhar's ability causing you to resolve another card, finish resolving each of the mythos cards that were drawn. Start with the one most recently drawn and proceed in the order opposite to that in which they were drawn.
When resolving a mythos card that opens two gates, do not advance the doom track, but open the gates one at a time in the order in which they appear on the card. So, it is possible for Zhar's ability to create a string of mythos cards from the first gate and then, after all of the cards in that string have been completely resolved, to create a second string of mythos cards opening the second gate.
The mythos ability of each card is resolved after the gate opens. So, for determining which environment card takes precedence:
The mythos ability of each environment mythos card replaces previous environment cards. (The earliest environment drawn in a string of mythos cards will take precedence over others because it will be the last environment resolved. Hopefully that bit of bookkeeping makes sense.)
For determining which rumor card takes precedence when resolving a string of mythos cards:
Ignore the mythos ability of rumor cards if a rumor is already in play. (So if no rumor was in play before resolving this string of cards, the last rumor card drawn will be the only one put into play since it will be resolved before any other rumors.)
Hopefully that provides a not-too confusing model of how to handle Zhar's ability.
Associate Creative Content Developer