Learn Swedish: Egentligen låtsas de bara att de är vänner. - Actually, they only pretend that they are friends.

Because the sentence starts with the adverb egentligen (actually). Swedish strictly follows the V2 rule, meaning the finite verb must be the second block of information in a main clause. Since egentligen takes the first spot, the subject (de) swaps places with the verb.

Låtsas ends in an -s. Is it a passive verb?

No, låtsas is a deponent verb. This means it always ends in -s but has an active meaning (to pretend). Other common deponent verbs you have likely seen by now are hoppas (to hope), andas (to breathe), and minnas (to remember).

Since this lesson is about som om (as if), could we say låtsas som om here?

You can, but it is slightly repetitive. The verb låtsas (to pretend) already sets up an unreal scenario, so it usually just links with att (that) followed by a normal clause: att de är vänner. If you want to use som om (as if), it sounds more natural with a verb like to act or to look: De ser ut som om de vore vänner (They look as if they were friends).

I sometimes confuse egentligen with English words. Does it mean eventually?