I have used a home daycare for both my children although my now 4 year old recently switched to a preschool. Most of the questions you posted should be addressed in your handbook/contract. They warrant pointing out as well as having the contract signed and each parent having a copy of.
I was always charged for the day regardless of if my child attended because that spot is theirs and the provider is limited on the number of children they can have in their care...if they are allowed five children and have five children enrolled, they have to turn number six away...parents have to pay for thier child's spot. The only exceptions to this were when/if the provider had a policy where there was a one week each year that you could schedule an unpaid vacation week (for instance, planning a family vacation and you give proper notice that your child would not be there thus allowing the provider to fill the spot for that week or plan their own vacation) and/or if they exceeded their paid vacation/sick days.
Of course I don't like paying for days they miss but I understand it...just like my job, they get paid leave days and holidays. The ones I have the most trouble with is the extra holidays (my most recent provider had all the "state" holidays some that even the schools were closed for) or excessive extra days. Those days more than ate up all my leave time so then when you added her sick or emergencies days I was missing a lot of time, not to mention if/when my child was sick. If I didn't miss work, it cost me time and money to transport my child somewhere else.
On the rare occasion I was late, I was not charged because it was only a few minutes and I would call before I was late. It was always because of getting out of work late or a traffic issue (I worked on an Air Base and sometimes it would go on lock-down). She chalked that up to an emergency and didn't charge; however, she did charge for late pick-ups as a rule but rarely implemented it.
If I was out sick, my daughter still attended but would get picked up a bit early. If the parent is sick, the child is better off being at daycare and the parent getting rest....besides, they are paying for childcare and that spot so unless you stipulate you only care for the child while the parents are "at work" then how/why would you not let the child come if they parents were home sick?
If they are late picking up due to "goofing off" (especially if you are charging for late pick up) the only thing you really can say is "I don't mind the occasional late pick up if there is an urgent issue like work or an emergency or if you schedule it ahead of time but this is getting to be an all too often occurance and it needs to stop". I can get why a parent would make a quick errand on the way home or stop to do something at home but the other things or being late for any of the rest is beyond me.