why are we using 自動車 instead of 車?
Either would be fine, they're just trying to expand your vocabulary. Jidousha is like automobile, and kuruma is like car.
自動車 is often used in newspapers, business and advertising, and the vocabulary is in JLPT N5, so it helps to know. 車 is fine too, mind!
Aahhh i wish they could warn us when they are switching words on us
Can we say 新しい自動車は母をかいました?
That's saying "a new car bought my mother". The particle を signals what is being bought.