Learn Danish: Fru Nielsen underviser i dansk. - Mrs. Nielsen teaches Danish.

In Danish, you don't just teach a subject directly. The verb underviser (teaches) requires the preposition i (in) when mentioning the subject being taught. So literally, she teaches in Danish.

Could I use the verb lærer instead of underviser here?

Yes, but they work slightly differently. The verb at lære means both to learn and to teach. If you use it to mean teach, you usually drop the preposition i. However, underviser specifically means to instruct or give lessons in a subject, which makes it the standard choice for describing a teacher's profession.

Why isn't the language dansk capitalized?

Unlike English, Danish does not capitalize the names of languages, nationalities, or adjectives related to countries. They are always written in lowercase unless they are the very first word of the sentence.

Is it common to use titles like Fru (Mrs.) in Denmark today?

Not really. Denmark is a very informal society, and students today almost always call their teachers by their first names. Using Fru (Mrs.) or Hr. (Mr.) sounds quite old-fashioned or overly formal, though you will still see it in older texts or historical contexts.