Actually, IIRC, being "illegal" has no bearing on your scenario: If a gun is in plain view, whether in a car or even a home, and the person is suspected of murder, a warrant is not needed according to our current law.
That depends. If I show up at the suspect's house, and detain him for questionig, and notice a gun in his car as I walked by, I would certainly need a warrant. If he's been stopped, and it is noticed, I have more leeway.