If you have Auditing turned on, you can check your audit log for login failures in system management portal. That will tell you why the login failed, which might point you in the right direction.

Does the test user account have the right security resources to access the database you're trying to log into? The quick easy way to check if you have a security-related issue is to give the test user the %All role and see if the issue goes away. If it does, you need to figure out what resource/role is missing for the user account. You don't want to permanently leave the %All role on there.

Yes. You can use a variable name starting with ^, like ^MyGlobal, and it will be a global. You will not be able to access it via SQL, but you will be able to see it with the globals in the system management portal. You can also reference globals in a different namespace by using ^|"namespace"|MyGlobal.