1. When it doubt, assume that a student's question or suggestion is sincere.
I'm not here talking about accepting excuses for tardiness or late papers (although this might apply in those situations). I'm talking specifically about suggestions that students make about the course or questions they have about the content of the course. Once I had a student suggest that the students grade each other's papers, instead of me grading them. I dismissed that suggestion out of hand and in a way that probably hurt her feelings. As it turns out, it would have been unworkable and probably not the best way to go about papers in that particular class. Still, I could've been nicer about appreciating her suggestion, because it was made in good faith.
Similar thing with questions. Students almost never ask questions unless they sincerely want an answer. (There are exceptions, to be sure, but in general, even something that seems obvious may not be obvious to the student.)
2. There is not such thing as 100% fair lateness/tardy/absent policy. No matter how hard you try, nothing you will do when it comes to exceptions to the course requirements is going to be completely fair to everyone in the class.