Below are the answers to your questions:
1- Is there a way to see the timestamp and method a subscriber used to unsubscribe? (list header vs. footer link)
Ans: You can see the timestamp in the Broadcast stats however, the method of how a subscriber has been unsubscribed isn't published yet but you can put this request in the feature request thread and we will put it in the development pipeline https://community.mumara.com/forums/feature-request.14/
2. Does Mumara auto-unsubscribe users that soft bounce a certain number of times?
Ans: Currently this auto mechanism isn't available in Mumara but you can achieve it through some manual processes like segmenting the soft bounces and then unsubscribing them through a trigger. However, we will also put this feature in the development queue once you post it in the feature request thread.