Learn Dutch: Wat zij opofferen, is hun vrijheid. - What they sacrifice, is their freedom.

In this pseudo-cleft sentence, the entire first clause (Wat zij opofferen) acts as the subject of the main sentence. Since Dutch follows the V2 (verb-second) rule, this whole clause takes up the first position, meaning the main verb (is) must be in the second position, right after the comma.

What is the difference in emphasis between this sentence and Zij offeren hun vrijheid op?

While both sentences mean they sacrifice their freedom, the pseudo-cleft structure (Wat... is...) puts a heavy focus on the outcome. By delaying the object until the end, it creates a bit of suspense and specifically highlights that it is their freedom they are giving up, as opposed to something else.

Opofferen is a separable verb. Why isn't it split up here like it is in Zij offeren iets op?

The phrase Wat zij opofferen functions as a subordinate clause. In Dutch subordinate clauses, the verb is sent to the end. When the conjugated part of a separable verb is pushed to the end of the clause, it rejoins its prefix, so they are written together as a single word.

Could I use ze instead of zij in this sentence?

Grammatically, yes. However, because this sentence structure is used to create strong emphasis, a speaker might also want to emphasize exactly who is doing the sacrificing by using the stressed pronoun zij. If the identity of the people isn't a focal point, ze works perfectly well.