Is my marriage to a Christian woman, which was solemnized inside a car in the presence of two witnesses, valid, especially since a dowry of an unreal gold dinar was named? Do I have to pay a real dowry despite the wife's refusal?

Marriage is not valid inside a car, nor is it permissible for a foreign woman to sit with non-mahram (definition) men. Marriage to a chaste woman of the People of the Book is permissible, though disliked. Its conditions are the same as those for marrying a Muslim woman: a guardian and two witnesses. The dowry is not a condition for the contract; she is entitled to a dowry equivalent to that of her peers, and she may waive it. If the marriage is concluded with its conditions, including the guardian, then it is valid, and the dowry is waived if the wife relinquishes it.