I watched the last module hoping to find answers to my paying questions, but it goes through it too quick focusing on types of payment. My questions: My project is a whole book but I will be paying in parts, although we've set an X price for the whole. How do I do that? Should I use the milestones part? How does it work?
Yes, milestones is what you need.
One milestone = one deliverable. You put money into the escrow, the freelancer writes X words, you check everything and if happy, you release the milestone. Then you do this again.
You can also simply use separate contracts. It doesn't cost any more to do that.
You can set up a contract for Step 1.
And a new contract for Step 2.
And another for Step 3.
If it turns out that you don't want to work with the same freelancer for Step 2, then you can easily hire somebody else for Step 2.