Hi! Played it, really nice little game.
1. Was the first minute clear without tutorial text? Yes, very easy to understand, I knew what to do right away.
2. The Inspect button is well visible, and the help at the start of the game made sure I noticed it.
The rules and the visitors never felt unfair to me, and the length of the days felt right. I lost on day 4 though, so I can't tell you about day 6, haha. Maybe the difficulty already ramps up a bit before day 6?
One suggestion: when a visitor is denied, it would be nice to see why (which rule they broke). It would help to learn from mistakes and understand the rules better, especially as they get more complex in later days.
Nice job, and good luck with the next steps!