Learn Swedish: Varför gråter barnet? - Why is the child crying?

Just like with other question words you have learned, Swedish keeps the verb in the second position (the V2 rule). So you start with the question word (varför), follow it immediately with the verb (gråter), and then put the subject (barnet).

The translation says "is crying", but where is the word for "is"?

Swedish does not have a separate "is doing" tense. The single verb gråter translates to both "cries" and "is crying". You never use är (is) plus another verb to show ongoing action in Swedish.

Why does barnet end in -et here?

The -et ending is the definite article, making it "the child" instead of just "a child". Because barn is an ett-word, you add -et to the end to say "the". If it were just "a child", it would be ett barn.

If someone asks a varför question, how do I start my answer with "because"?

To say "because" in Swedish, you usually use the phrase därför att or just för att. For example, you might answer För att han är trött (Because he is tired).