Eat as much fat is you need to feel satiated and to make your foods taste good. There are people who do PP who eat a lot of fat, and that works for them. High fat intake makes me feel ill. In any given week 60 - 65% of my calories come from fats.

You are allowed to eat anything, whether listed in the book or not. You just have to find the correct amounts of those foods to give you 7 - 10g of carbs. Coconut milk is also okay.

The biggest change from Atkins is getting accustomed to remembering that all foods are allowed, often in very small amounts, and that it is up to you to decide what to eat. You have it exactly right -- as long as you do the math it's okay. The other thing, of course, is watching how you feel after eating different carbs. If it makes you crave more carbs in general, or more of that one carb, then you know it is something you need to avoid.

One important carry over from Atkins is eating carbs with protein and/or fat. A snack that is essentially all carbs is really not a good idea.