Ok, so these quests are just to qualify for the third quest, which will decide the house, and that quest gets done once a day till someone gets it? Something like that?
From what I understand from what the letter about the housing and What Cal said.
Cal said, if I remember, and I might have miss read as I think it's wrong, that the first tier (The Lantern, I assume) got you into the housing quest.
The second Teir (finding the spots). Is essentially for items, a new spot will be revealed each day until the actual house spot, April 12th, will be revealed.
The third quest is PROBABLY when you're actually entered in it, and is repeatable once a day for the rewards, completing it more than once does not increase your chance at getting it, just increases your chance at a better reward for doing the quest.
Hope that helps.