First of all - the police do not issue warrants - only the judicial system can issue warrants on which the police then act. (e.g.- A Magistrate, a Justice of the Peace - a Judge - etc). The person may have appeared before court and swore under oath that their report was true.
It depends on what jurisdiction you are in. In many jurisdictions, police are legally permitted to enter a premises whenever they have "probable cause" or "reasonable cause" to suspect that there is an illegal activity in progress (for example, if they could hear someone being attacked). Some laws also may allow police to enter a house without a warrant if they are in the course of investigating a specific crime.
A trespassing warrant does not have an expiration date unless the person who has requested the warrant withdraws it. A trespassing warrant a valid document of someone requesting another person to not enter onto their property without permission.
Someone claimed that someone else threatened to resign because of some offense of some kind. It's very vague without context.
call the state police and ask
A warrant is an order for an arrest issued by the court. But many arrests do not need a warrant. If you punch someone in the face, and police are called, you will be arrested without a warrant, and one will not be needed. If say, you failed to show up in court, then a warrant for your arrest will be issued, to alert all officers that you should be arrested on sight. So the warrant itself is not the thing 'allowing' you to be arrested.
It does not seem reasonable or possible.
No. If the search warrant is invalid and they illegally searched you or someone you know (like without reasonable cause, or without the warrant) then they can't use any evidence against you. To the best of my knowledge, anyways. I don't know how many ways a search warrant can be wrong though...if they were searching for like, pot, but found cocaine, they CAN use that though. Or a gun, or something like that. If they have the warrant, they can use it. If they searched without the warrant, its invalid and inadmissible 100%.
Probably not. If the police are actively investigating a complaint (noise complaint) then they are likely within their rights to enter the premise where the violation is occurring.
Without a warrant you must find reasonable grounds to arrest someone, whereas with a warrant your reason to arrest the suspect already exists. Without a warrant a Police Officer can arrest anyone without permission of a Magistrate as long as they follow the correct procedures so their arrest is lawful, which is unlike an arrest with a warrant where you must be granted the warrant to be able to arrest that person. Without a warrant, a Police Officer can mess the arrest up and make it an unlawful arrest but with a warrant it is very unlikely that they make it an unlawful arrest.
It is illegal to video anything in someone's home without their knowledge and permission, unless you have court authority, such as with a warrant.
Kind of unlikely. If/When they run your name into the sytem to check on you, the warrant will probably show up, and you'll be arrested.
Police do not necessarily need a warrant to arrest someone. Basically an arrest means that they have strong reason to believe that someone has broken the law. A warrant allows them to arrest the person on sight even if they are doing nothing wrong at the time. If you feel like the arrest is unjust your best option is to get an attorney.