Can a warrant be requested to search your home after a routine traffic stop

A friend of mine was a passenger and the car was stopped for speeding . They pulled over and my friend the passenger showed his license because the driver left theirs . My friend the passenger was asked to get out of the car and was searched . My friend had drugs on him because he uses drugs. A warrant was requested. They bring my friend back to the house and the search of the home found no drugs, money . My friend had no warrants . 1 st Can you arrest a person at one location request a warrant and take them to that location? 2nd was he illegally searched ? He was not the driver there was no smell of drugs or a crime being committed.?