Learn Swedish: Allt har tystnat, därför kan vi sova. - Everything has fallen silent, therefore we can sleep.

It comes from the adjective tyst (quiet or silent). Adding -na to the end of an adjective creates an "inchoative" verb, which simply means a verb that describes a change of state, or "becoming" something. So the infinitive tystna means "to become quiet" or "to fall silent".

Why does tystnat end in -at here?

It is in the supine form because it comes directly after the helper verb har (has). Verbs that end in -na almost always belong to verb Group 1. This means they take -ade in the past tense (tystnade) and -at in the supine (har tystnat).

Why is the word order kan vi instead of vi kan?

The second clause starts with the adverb därför (therefore). Because Swedish strictly follows the V2 (verb-second) rule, the verb kan must be the second block of information in that clause, which pushes the subject vi to the third position.

Could I use alla instead of allt at the beginning of this sentence?

No, because alla means "everyone" or "all of them" (referring to specific people or plural, countable things). Allt is used here to mean "everything" in a general, uncountable sense, referring to the entire environment around them.