Learn Dutch: Ik leg hen nu het project uit. - I am explaining the project to them now.

This is because uitleggen (to explain) is a separable verb. In a standard main sentence, the core verb (leg) takes the normal verb position right after the subject, and the small prefix (uit) gets pushed all the way to the very end of the sentence.

The lesson says both hen and ze mean "them". Why use hen here?

Both hen and ze can mean "them" when referring to people as an object. Hen is the full, slightly more formal or stressed form. Ze is the unstressed, everyday form. You use hen here because it is a bit more formal, or if you want to put slight emphasis on the fact that you are explaining it to them specifically.

Why is nu (now) in the middle of the sentence? In English it goes at the end.

In Dutch, adverbs that tell you when something happens (like nu) usually come early in the sentence. They typically go right after the main verb and any small object pronouns (like hen).

Why does hen come before nu, but het project comes after it?