No, not based solely on rumor or hearsay. However, if they look into the information contained in the rumor to determine the truthfulness of it, it is possible that their investigation might disclose sufficient probable cause to arrest you for an offense.
Quite often these "rumors" turn out to be what is known as "leads."
It depends on what you mean by rumors, but they can say you're suspected of a committing a crime even though you have not been arrested
You have until there is time for a judge to hear the case.
an arrest warrant.
no, you can not. but police can arrest you.
The police can arrest you ANYWHERE.
You could try a citizen's arrest but the police man may refuse to be arrested. It is only a warranted police officer that is empowered by society to forcibly arrest someone.
Police officers can arrest you
No
The policemen were arresting the burglars after finding them red-handed.
Yes, of course. An arrest warrant is a command from a judge to arrest a person. Usually a police officer has no choice and must arrest.
They arrest you if you have possesion of it.
Yes
There is no such thing as an illegal argument so the illegal police will not arrest you.