Private
It isn't my fault if poor people don't care for their children. People all have their own duties, don't they? If you're born to a pureblood line you're responsible for the community and you're supposed to act accordingly. It isn't unfair, and it isn't arbitrary - our magic is stronger.
Yes, which is another reason for being polite, isn't it? I should respect my elders. Women in Everdale mostly dress like women, but if you ever venture outside it you'll see that most of them have the same ideas as you. It's peculiar, but one gets used to it. It isn't as bad as having them dress as if they belong in a brothel.
The punishments depend on the crime, naturally. Here's an example, though: if I'm insolent at school, they'll hex me. I'm not a coward, I can bear it, but I'll say that it hurts. I'd rather they didn't. Once the marks are gone there isn't any damage, though. Boys at muggle schools probably get beaten with sticks and locked in cupboards and all sorts of horrid things and that's worse.
How do you justify taking your 'prizes' from people who haven't done you any harm and probably worked hard to get them, though?