Is it illegal to arrest without warrant of arrest?

Yes

ANY offense which occured in an officers presence, or any felony crime for which your name and/or description has been flashed over the police communications systems.

The moment any arrest warrant is signed by the judge it becomes an outstanding warrant. It may take a couple of weeks for the Warrants Division of the Sheriff's Office to enter this in their...

Yes.

Not if the officer has probable cause that the offender has committed a crime.