I like this approach: Common suggestions when first landing on the screen. I think your approach combining suggestions without even do the type will give users that you have some suggestions. Combining with list that can be search is a great idea.

To answer your questions:
> 1. How should the interaction model should work as they type (should the top autosuggest just be what's typed or should there be a done button that just submits what's currently typed, or both)

Quite confused with the options here. I think this is a very common pattern that you can copy the interaction. The most common is user type, then show suggestions, then user click on suggestions to apply. If there's no suggestions, then user can add the label they typed. If the label will be used repetitively, then can consider to save the new label that user typed.

> 2. Is it weird to have autosuggest, but show random (choosable) suggestions before even typing?

The goal for auto-suggest is to simplify the UX and interaction cost. Definitely a great idea on how to make it more contextual.