Hi there,
1) I don't really understand your question. But if you want to find all action groups that have been stopped to trigger alert instances by some reasons - no, you can get the data in email only (for example, if your notification action group is too noisy)
But if you are looking for disabled instances, just check all Action Groups assigned to Alert Rules.
2) Yes, you can get the data in alert instance itself. Just open a history tab in alert. Action Group is a hyper-linked url that includes all information about actions being used when an alert has been created, including email if it's configured.