Both are fine.....in exact terms I feel that 자동차 is automobile and 차 is car
차 can mean either car or tea, so when there is any doubt which one you mean you use the longer word instead to be specific.
Is anyone else just pronouncing it like they're playing that headphones game where you have to guess what the person is saying?
I believe you can use the naver dictionary to give a better pronounciation. The pronounciation in duolingo sounds a bit off to me sometimes.
I still have some difficulties to identify the difference between 자 and 차 pronunciation wise.
I was told the best way to think of this is to alternate pronouncing both the short j sound and the "ch" sound and notice how the short j sound is very similar to the "ch" sound. This is the concept behind the pronunciation. How to pronounce it in a given context will have to be up to someone else to explain, but with 자동차 it is pronounced with more of the "cut off" short j sound, or the "ch" sound if you will. And in something like 남자 it sounds more like the plain short j sound.