Is it obligatory to fulfill the vow, "By Allah, the wedding car for your marriage is on me, and it will be a latest model BMW," despite the difficulty of providing the car except by renting it, and the groom has not yet been informed of this, and his wedding date is approaching?

What you said to your friend is an oath, not a vow (nadhr). Allah does not burden you with what you cannot bear. If you do not do what you swore to do at the wedding, then you must pay atonement for breaking an oath. Even if what you said was a vow and you were unable to fulfill it, the ruling would not differ.