To measure notifications, thus determining which notification is the source of which traffic, you will need to declare a custom marketing campaign in the interface and tag your notifications accordingly (Android and iOS documentation).
To measure crashes, you should not need to do anything; the information is automatically gathered by our SDK once the app is reopened. There are specific dimensions and metrics in the "Apps" category in Data Query that will allow you to view related data. To easily view these metrics, go to the Dashboard template library and select "Mobile - App Analytics". This will deploy the analyses and metrics for the selected sites.