막차←마지막 차 (literally last vehicle, but can refer to any mode of transportation service like train, bus, or van)
Bus is also correct.
What time is the last one? should be accepted as it does not tell which mode of public transportation is on the topic.
I see what you mean, and I don't think that you're wrong. The Korean does specify a vehicle though, 차 車。 If the context were clear, your translation would definitely be correct.
The 막 in 막차 (lit. last vehicle) is the same root used in the word 막내 (maknae, lit. lastborn).
(이)야 is a casual "이에요/예요" which is for nouns.
Head canon: this also refers to that last cup of tea in a restaurant, after you're totally done eating.