If the police officer has probable cause that a crime has been committed, they may take appropriate action to handle the situation, which includes issuing a ticket.
Where this occurs is irrelevant.
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It depends on wether or not the owner of the property allows local city police (or in the event that the property lies in un-incorporated parts of a city) county sheriff to enforce public traffic laws on their property.
It depends on the way the law is written in your state. In some (all?) states the regulation is worded so that it is effective and enforceable ANYWHERE in the state, and that includes private property.
If it can be heard off of that property, and is determined to be a nuisance, yes.
Not in the UK, but the private land owner may be able to clamp your car and charge you to have it released.
Yes, particularly if the owner has already given the police permission to do so. Just because you are on private property does not mean you can violate the law.