Learn Portuguese (Portugal): Eu estava a olhar para o horizonte quando o nevoeiro denso chegou. - I was looking at the horizon when the dense fog arrived.

This is the classic "interrupted action" structure. You use the past continuous (estava a + infinitive) to set the scene with an ongoing background action ("I was looking"). Then, you use the preterite (chegou) for the sudden, completed event ("arrived") that happened in the middle of it.

In English we say "looking at". Why does this sentence use para instead of a?

In Portuguese, the verb olhar (to look) requires the preposition para when indicating the direction or target of your gaze. While a can mean "at" in some contexts, "looking at" is always translated as olhar para.

Could I place the adjective before the noun and say denso nevoeiro?

You could, but it changes the tone. In everyday Portuguese, adjectives generally follow the noun (nevoeiro denso) when describing objective, physical traits. Placing it before the noun (denso nevoeiro) is grammatically correct but adds a poetic, dramatic, or literary flair.

Since this lesson covers probability, how would I change the second half to say "the dense fog must have arrived"?

You would say ...quando o nevoeiro denso deve de ter chegado. Using dever de + the compound infinitive (ter chegado) expresses a strong assumption about a past event. Remember that in European Portuguese, adding de clarifies that you mean probability ("must have") rather than obligation ("had to").