STORY SPOILER!
I think I made a huge mistake.
A new month started and Flayn went missing. After I ran around and talked to everyone I chose to enter the knights dorm (?) because it said my exploration time would end and I had nothing else to do. Then a fight started and Flayn was found. A new month began after that and I think I skipped 3 whole weeks of exploring and fighting...
Maybe I could have ended the week just by pressing L or would that also trigger the Fight/Story?
Edit: This "problem" is more or less solved. Thank you all for replying! Feel free to comment your experiences on this topic anyway.