Translation:I went to a department store by car.
It needs to be in past tense ("went"), but otherwise it's fine. You are correct that it's still not accepted in that word order, so you should report it.
I said "I went to the department store in a car" and it wanted "by car". They mean the same thing to me in this context. Should my answer be considered correct?
That's the only way I'd feel comfortable saying a sentence like this "I drove there in a car" "I got here in a taxi" "I flew to another country in an airplane" saying by car just kind of feels funny in my mouth. I think it's worth flagging, and "in a car" should be accepted
It's just some particle witchcraft. A direct translation of it would be more accurately, "by way of" but that sounds weird in most context so technically they mean the same thing in English but the direct translation is a little more informative.
I didn't put an "a" there. Should I did? It didn't make much differences actually
It is not propper english to say "I went to department store". It needs to have "the" or "a".
"I drove to the department store"
Not accepted. It's not literal, but I feel like the car is almost implicit in this sentence (not many other things you typically drive in such a scenario) and it's a fairly natural way to express the same idea. Or is it? Not a native-speaker.
I agree! This is a pretty common way of translating those types of sentences (english has lots of very specific verbs). In my language we would say "I went there by car" as well but in english "I drove there" is much more common and natural. I know this is a Japanese course but i believe it should be accepted!