> Can a bar refuse entry to children?

If it's legal for children to enter a bar, I don't see why a bar should be able to refuse entry to children.

> Can a cinema kick someone out for talking during a movie?

If they're causing a problem for other people in the cinema and refuse to stop, sure. A right to be access a product or service shouldn't override other people's right to get what they paid for.

So for "lawful manner" in my above post: "lawful manner, or manner that doesn't negatively impact other customers".

> Can a dance club have a dress code?

If a club wants to only allow a specific type of member then it should be a private club.