Can't change authentication mode from Windows to both SQL Server and Windows
The EXECUTE permission was denied on the object
  'xp_instance_regwrite', database 'mssqlsystemresource', schema 'sys'.
  (Microsoft SQL Server, Error; 229)


You can fix the problem by granting the user direct access to the procedure.

USE master
GO

GRANT EXECUTE ON [sys].[xp_instance_regread] TO [DOMAIN\USER];

--To veriy that the user has been granted the privilege
EXECUTE AS USER = 'DOMAIN\USER';Select * from fn_my_permissions('xp_instance_regread','Object')



  Cannot alter the login 'sa', because it does not exist or you do not
  have permission.


Error message saying that, You do not have administrator's permissions

Log into SQL Server Management Studio as an Administrator, because only admin user has permission to change passwords for users.

How to change sa user password see here: How to change a password for the sa user in MS SQL? and this link