Learn Danish: Forstår lægen engelsk? - Does the doctor understand English?

Danish doesn't use helper words like "do" or "does" to ask questions. Instead, you just start the sentence with the verb. Putting the verb (forstår) before the subject (lægen) makes it a yes/no question, so this literally translates to "Understands the doctor English?"

Why does the word for doctor (læge) have an -n at the end here?

That attached -n is how Danish says "the". The base word is en læge (a doctor). To say "the doctor", you move that en to the end of the word, making it lægen.

Why is engelsk written with a lowercase letter?

In Danish, you do not capitalize the names of languages or nationalities. Even though it is capitalized in English, it stays lowercase engelsk in Danish.