You have 7 days total to explore Dragonholt, not 7 days between each quest.
re Questing & Dragonholt time:
Spoiler (click to reveal)
Questing will eat up a bit of your Dragonholt time. When you complete a quest, it will direct you to a Dragonholt entry to cap it off, and that entry will tell you how much time (if any) to mark off on the Dragonholt sheet.