The Dashboard has a lot of decent information. This article has a list of some of the information available and includes some of the queries used by the  dashboard:
Answering Questions with the AlwaysOn Dashboard

This lists what is likely the most common alerts you want to set up for AOAG:
Configure SQL Server Alerts and Notifications for AlwaysOn Availability Groups

For some of the other things you mention, take a look at the DMV sys.dm_hadr_database_replica_states. I think that has the other information you want - write whatever queries meet your needs, write a job, schedule it for however often, etc.

There are also some Perf Mon counters available that you can schedule in the alerts or you can query those in sys.dm_os_performance_counters.

Sue