They can search for what is stated in the search warrant. In some states if they find something else, say illegal drugs sitting out in the open and easily seen, they can confiscate them and arrest...
Yes, if it is specifically stipulated in the warrant or the wording of such is "entire residence and/or business, and/or surroundings and so forth is stated.
The judge that okays the affidavit and signs the warrant may have a log book in which the warrant is recorded, or the agency that is seeking it, may also have one, but I am not aware of any legal...
Actually the police don't necessarily have to show the warrant to anybody. In fact, to execute a search warrant it isn't even necessary for a resident or occupant of the premises to be present.
Judges do not search anything or anybody. The process of applying for and issuing a warrant is as follows; Law enforcement conducts a criminal investigation and develops certain facts about something...