Only law enforcement can enforce the trespass. But you are trespassed when informed by a person with authority over the property that your presence is not welcome there. If they fail to leave, you can follow up in the courts.

Owner / caretaker of any property can trespass anyone on their property. Law enforcement included. Which is why they need a warrant.

Hmm, I would check your local law. That is not how it generally works. If someone is on your property and you tell them to leave and that they are trespassed, then they have to leave. Failure to leave is almost always a crime in progress.