Learn Italian: Scrivo una frase in italiano. - I write a sentence in Italian.

In Italian, una frase almost always means a complete "sentence." It's a false friend for English speakers! If you want to talk about a "phrase" (a small group of words), you would usually use un'espressione.

Why is it in italiano instead of nell'italiano?

When you talk about doing something in a specific language (like writing, speaking, or reading), you just use the simple preposition in without the definite article. So you say in italiano, in inglese, in spagnolo, and so on.

Why isn't the word italiano capitalized here?

Unlike in English, names of languages and nationalities are not capitalized in Italian. You only use a capital letter for the name of the country itself, like l'Italia.