Learn Italian: Perché torni presto oggi? - Why do you return early today?

It actually means both! In Italian, you use perché to ask a question ("why") and also to answer it ("because"). Since it is at the start of a question here, it means "why".

Where is the "do you" in this sentence?

Italian doesn't use helping words like "do" or "are" to ask questions. The verb torni all by itself means "you return", "do you return", or "are you returning". You just raise your tone of voice at the end to make it a question.

Why is the word "you" (tu) missing from the Italian sentence?

In Italian, the ending of the verb tells you who is doing the action. The -i ending on torni (from the verb tornare) already tells us that "you" are doing it, so adding tu isn't necessary unless you want to add special emphasis.

I've seen presto mean "soon". Does it mean "soon" or "early" here?

Presto can mean both "early" and "soon" depending on the context. In this sentence, asking why someone is coming back presto oggi makes the most sense as "early today".