Learn Swedish: Mordet hände i natt. - The murder happened last night.

I natt can mean either 'last night' or 'tonight' depending on the verb tense! Because the verb here is hände (happened) in the past tense, i natt refers to the night that just passed ('last night'). If the verb were talking about the future, it would mean 'tonight'.

If 'last night' is i natt, is 'yesterday' i går?

Exactly! Swedish uses the preposition i for several specific past time expressions. I går (yesterday) and i morse (this morning) are other common examples. Notice that they are traditionally written as two separate words.

Why do we use the simple past hände instead of har hänt (has happened)?

In Swedish, whenever you mention a specific, finished time in the past like i natt, you must use the simple past tense (hände). You would use the 'has done' form (har hänt) only if you didn't mention exactly when the event took place.

Why is it mordet and not just mord?

Mord (murder) is an ett-word. To make it definite ('the murder'), you add -et to the end, giving you mordet.