If deputies raid a house looking for evidence but find none, can they still arrest the person? Are there any cases you can recite? If deputies say a crime happened at 3 am, can they have a search warrant by 6 am?

In the United States, a search warrant and arrest warrant authorize different courses of action by police. During the execution of a search warrant, police officers do not have the authority to arrest anyone who happens to be in the building being searched in the absence of probable cause, though—on the basis of reasonable suspicion—can temporarily detain them for purposes for determining identification and other basic facts (see the 1968 case of Terry vs. Ohio). Reasonable suspicion is a lower standard than probable cause.
Further, police must extend a basic level of courtesy to the non-suspect occupants of a building being searched. In the 2009 case United States vs. Thompson, the Supreme Court determined that it was unlawful for authorities to detain a non-suspect occupant of a searched premises for five hours and refuse to permit her to dress.
However, if during the course of the search, officers find probable cause evidence linking one or more occupants of the building being searched to a crime, then they can arrest those persons.
Whether a law enforcement officer can obtain a search warrant in three hours depends on a variety of factors, such as whether sufficient evidence to establish probable cause—which is necessary for a court to issue a search warrant—can be gathered during that time. In most areas in the United States, a judge, magistrate, or court commissioner is either available or can be made available twenty-four hours a day to issue warrants.