No, but you will never make enough to afford one if you don't. even if you do have a vehicle, you might not be able to afford to maintain it.
I have a 1999 Buick Park Avenue have had it for 2 years
Yes. Preferably a hybrid.
Yes. Preferably a hybrid or a small 4 cylinder car
Yes. transportation is not provided.
Yes, must have your own transportation
Yes, you need your own vehicle to do deliveries.