Learn Danish: Pludselig bankede en fremmed på døren. - Suddenly a stranger knocked on the door.

Because of the Danish V2 (verb-second) rule. The sentence starts with the adverb Pludselig, which takes up the first position. The verb bankede must come second, so the subject en fremmed gets pushed to the third position.

Isn't fremmed an adjective meaning foreign or strange? How does it mean a stranger here?

In Danish, you can often turn an adjective into a noun to describe a person simply by putting an article in front of it. Here, adding en turns the adjective fremmed into the noun phrase en fremmed, meaning a stranger.

Why is the preposition på used here instead of just saying bankede døren?

The fixed expression for knocking on a door in Danish is at banke på. If you left out på and just said bankede døren, it would sound like you were physically beating or hitting the door, rather than knocking to get someone's attention.

Since Pludselig is used as an adverb here, shouldn't it end with a -t?

It can, but it doesn't have to. The official Danish spelling rules accept both pludselig and pludseligt as adverbs. You will often see it without the -t, especially when it starts a sentence.