Learn Swedish: Jag vet hon lurar alla sina vänner. - I know she is deceiving all her friends.

Yes, the word att (that) has been omitted. In spoken and informal written Swedish, att is often dropped when it connects a main verb like knowing, thinking, or saying to a subordinate clause. You could absolutely say Jag vet att hon lurar..., but leaving it out is very common and mirrors how we drop 'that' in English (I know she is...).

Why does the sentence use sina instead of hennes for 'her'?

Because sina is a reflexive possessive pronoun, meaning it points back to the subject. If the sentence used hennes vänner, it would mean she is deceiving some other woman's friends. Using sina makes it clear she is deceiving her own friends.

Wait, the very first word is Jag (I). Shouldn't a reflexive pronoun refer back to the main subject?

Not in this case! Reflexive pronouns like sina refer back to the subject of the specific clause they are in. This sentence is made of two clauses: the main clause (Jag vet) and the subordinate clause (hon lurar alla sina vänner). Inside that second clause, the subject is hon, so sina strictly belongs to her.

How does the word order work in the phrase alla sina vänner?