The answer to your question is not as straight forward as you may think. First off, unless you have already obtained a copy of the officer(s) statement, you are only assuming that one of these reasons was used as justification for the search. Since you were not even there, you can only assume that the officers did not see or smell anything to prompt the search, that no permission was given, or that there was not some other justification for the search.
With those caveats, I will try to answer your questions. First, arrest on a warrant will generally not justify a search of a vehicle incident to the arrest. However, “search” legally has some different meanings. Depending on what the warrant was for, the arrestee’s criminal history, some circumstances encountered during the arrest, the officers may have been justified in conducting a “protective sweep” of the vehicle for weapons. If other contraband is discovered during this sweep (presuming that the officers conducted the sweep as lawfully allowed) it can be seized and would be admissible as evidence – at the very least, it would provide probable cause for the vehicle to be impounded and held while a warrant is obtained.
Similarly, an investigation into DUI would not generally provide legal reason to search the vehicle. However, an arrest for DUI would allow for a search incident to arrest for any evidence related to the DUI arrest (alcohol containers, drugs, etc.). Was the driver arrested or just investigated and released?

