Answer to Question 1
To satisfy the Fourth Amendment's reasonableness requirement, arrests require both probable cause before, and a reasonable execution during and after, the arrest. Probable cause requires that an officer, in light of training and experience, knows enough facts and circumstances to reasonably believe both that: (1) a crime has been, is being, or is about to be committed; and (2) the person arrested has committed, is committing, or is about to commit the crime.
Answer to Question 2
The three elements of arrest warrants that satisfy the Fourth Amendment warrant clause are as follows: (1) a neutral magistrate who decides whether probable cause exists; (2) a sworn statement made by somebody who swears under oath to the facts and circumstances amounting to probable cause; and (3) the name of the person to be arrested (i.e., the warrant must identify specifically the person the officers are going to arrest).
As for the first requirement, that of a neutral magistrate, this requires the police to get approval from a neutral magistrate, who will fairly and accurately review the warrant before it is issued. Studies have shown that most magistrates devote little time to reviewing a warrant's sufficiency. They assume that the person swearing to it is being honest, and they tend to ask no questions about the warrant.
As for the second requirement of a sworn statement, also known as an affidavit, the Fourth Amendment requires that magistrates base their probable cause determinations on information sworn to under oath. The pain of perjury encourages truthfulness. If the affidavit establishes probable cause, the magistrate usually issues the warrant.
The final requirement, naming the person to be arrested, is part of the Fourth Amendment's particularity requirement. Thus the warrant should contain the name of the person to be arrested or, if the person's name is not known, a description by which the person can be identified with reasonable certainty.
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