Learn German: Hast du ein Auto? - Do you have a car?

The verb haben (to have) is slightly irregular in the present tense. For du (you, informal singular), you drop the b from the stem. So, it becomes hast instead of the expected habst.

Why is there no German word for "Do" in this sentence?

English uses helper words like "do" to ask questions (Do you have...?). German doesn't do this. Instead, you just move the verb to the very front of the sentence. Swapping Du hast (You have) to Hast du automatically turns it into a question.

Why do we use ein Auto and not einen Auto or eine Auto?

The verb haben always requires the accusative case for the thing being had. However, Auto is a neuter noun. For neuter nouns, the word for "a" (ein) stays exactly the same in the accusative case as it is in the basic nominative case. It would only change to einen if the noun were masculine, or eine if it were feminine.

Why is the word Auto capitalized?

In German, all nouns (words for people, places, things, and concepts) are always capitalized, no matter where they show up in a sentence!