Yes, an officer can legally do this even without getting a warrant.
When an officer stops a car for any legal reason, he or she can seize anything (anything illegal, of course) that is in plain view in the car. Once the car has been stopped for a legal reason, the officer must be able to seize evidence of illegal activity even without a warrant. There are two reasons for this. First, the evidence is in plain sight so no search of the car has been conducted. Second, the person who got stopped could easily destroy the evidence if the officer went off to get a warrant.
As stated in the link, yes. Although a search or seizure conducted without prior judicial authorization is "presumptively UNreasonable", there are noted exceptions.
If such is conducted without a warrant, then the govt. has the burden of demonstrating it falls into one of the exceptions.