Unless it's the very forst time you've fought that ED, it's completely random what area the second quest is in. It may not even show up until you do another quest in between, but don't worry, the damage still carries over.
Kirin is odd in that if you quest fail by time out, it carries the damage over, not sure about dying three times, but I'm fairly sure it doesn't carry over in that situation.
Personally, I do Low rank Kushala in the Guild due to it being in the town. Lunastra in particular I wait until I have the quest in the Tower, due to the area being more uniform, no lava and no need for hot drinks. again, Teostra I prefer to do outside the Volcano, and I NEVER do Chameleos in the Swamp. Can never find that damn tail in the top area...
...anything else you'd like to know about Elder Dragons?