Learn Dutch: Ik praat met ze terwijl ik de appel schil. - I talk to them while I peel the apple.

Terwijl (while) is a subordinating conjunction. This means it introduces a dependent clause, which pushes the conjugated verb to the very end. So, instead of saying ik schil de appel (I peel the apple), the order changes to terwijl ik de appel schil (while I the apple peel).

Wait, doesn't ze mean 'she' or 'they'? Why is it translated as 'them' here?

You are right that ze means 'she' or 'they' as a subject! But ze is also the unstressed object pronoun for 'them'. You could use the stressed form hen here, but in everyday spoken Dutch, ze is the most common way to say 'them' after a preposition like met.

The English translation is 'I talk' and 'I peel'. Can this also mean 'I am talking' and 'I am peeling'?

Yes, Dutch often uses the simple present (ik praat, ik schil) even when English uses the continuous form ('I am talking', 'I am peeling'). If you really want to emphasize that you are in the middle of the action, you could use the aan het + infinitive structure, but the simple present is much more common and perfectly natural here.

Does schil mean both 'peel' as a verb and 'peel' as a noun?