Can you write on a database that is a part of an always on availability group from the secondary replica?

Can a database be part of two availability groups?

You can use the primary replica of the second availability group in a distributed availability group to create another distributed availability group, even though the database is not in RECOVERY. You can also use the primary replica of the first availability group to create another distributed availability group.

How do you join a secondary replica to an availability group?

To join an availability replica to an availability group Expand the Always On High Availability node and the Availability Groups node. Select the availability group of the secondary replica to which you are connected. Right-click the secondary replica, and click Join to Availability Group.

Can you write on a database that is a part of an Alwayson availability group from the secondary replica?

Though you cannot write data to secondary databases, you can write to read-write databases on the server instance that hosts the secondary replica, including user databases and system databases such as tempdb.

Can we run DBCC Checkdb on the secondary replica of the availability group?

Checkdb should be run on both primary and secondary replicas.