AWS RDS MySQL database created but cannot create indexes or change collation
Solution:

a. create a user-defined parameter group and use it in the existing database instance instead of the default parameter group.

b. change the character set to utf-8. 


I can now create indexes and change the table and database collation.

So the issue was the lack of the user-created parameter group and a parameter group with the correct character set (i.e. utf-8).