I have had my account about 3 years, signed in many times without seeing any verification link.
If you are getting the account exists message that would suggest the account has been verified, The verification is only to confirm email address.
To sign in you need to enter correct email and password and also get the captcha right, nothing else.
If the account has been corrupted you will have little option than to create another with a different email.
As far as your name is concerned it is not a problem, that is only the profile name for the account. It is quite common for the hyphen to be disallowed as a special character, the underscore "_" normally works.
You would enter the correct details and a copy of your passport in the first stage of applying for a visa.