Is someone who spent the night in his car in Mina after arriving there late considered to have spent the night [there] or not?

Staying overnight in Mina on the eleventh and twelfth nights of Dhul-Hijjah is obligatory. The proof of its obligation is that the Prophet, peace and blessings be upon him, "granted permission" to Al-Abbas to forgo staying overnight, and a permission is only granted for something that is otherwise obligatory.

Whoever does not find a place in Mina after searching should sit in Muzdalifah at the end of the tents, and nothing is required of him, because Allah Almighty does not burden a soul beyond its capacity.