Officials in a school (and many other institutions) have a duty of care to ensure the safety and well being of people within the school. In some cases, the ability to search a student may be vital to ensure the safety of others. There are other situations where the ability to search students would be equally important. It is a power that should never be abused but to deny the power to school staff is to prevent them performing their duties in the best way possible.
It depends on the offense, but a person at school is not immune from arrest.
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.
No.
No, a police officer cannot issue a warrant for your arrest only a judge or court magistrate can do that.
It does not seem reasonable or possible.
A police officer must have probable cause in order to arrest someone. They can arrest a person if they see a crime taking place or if an arrest warrant has been issued.
no
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.
Probable cause or warrant
A person is "under arrest" when a police officer charges them with a crime and chooses to take them to the police station to be processed for it. For example, if someone commits a crime, they are technically under arrest when a police officer witnesses the crime or has a warrant for the arrest and tells the criminal "You are under arrest." Typical procedure after this is to put handcuffs on the criminal and read them their Miranda rights (you have the right to remain silent etc). Handcuffs alone do not mean arrest, but i'm pretty sure its illegal for a police officer to handcuff someone without grounds to arrest them. As a side note, the person doing the arrest does not have to be a sworn in police officer. In Citizen's arrest cases, anyone with arresting powers like a bounty hunter can also place someone under arrest.
If there is a warrant out for you and the police know where you are, they can arrest you.
If the officers can accurately identify the person wanted, or can verify a proper warrant then they will likely arrest you.
A "stop and frisk search," where police search you for their protection or incidental to an arrest; or when contraband is in plain view of the officer.