What is the last time for performing Fajr prayer, and is it permissible to pray in the car while going to work, or must one wait until exiting it after sunrise?

The time for Fajr prayer ends at sunrise. If you are unable to exit the car until after sunrise, you must pray Fajr inside it while seated, if you are unable to stand. Be sure to face the Qiblah as much as possible, and turn with the car if it changes direction. If you are unable to do so, then pray in the condition you are able to, by nodding, making your prostration lower than your bowing, in accordance with His, the Almighty's, saying: "Allah does not burden a soul beyond its capacity" (2:286) and "So fear Allah as much as you are able" (64:16).