Apple ID

My Apple ID is set up on an old email address that I do not have access to anymore.

1.

It depends on what you did with your 'old Apple ID'. If you have deleted it, it is no longer valid, it simply no longer exists and it no longer works.

To understand about a deleted Apple ID, see the Apple articles below:

How to delete your Apple ID account

How to delete your Apple ID account – Apple Support (UK)

Understand and control the personal information that you store with Apple

Understand and control the personal information that you store with Apple - Apple Support

2.

If you've ever requested to deactivate that old Apple ID, see

See -> How to deactivate your Apple ID account

How to deactivate your Apple ID account – Apple Support (UK)

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How to temporarily deactivate your Apple ID

Sign in with your Apple ID at privacy.apple.com on a Mac, PC, iPhone or iPad, and select "Request to deactivate your account". If you can’t see this option, it means that this feature is not available in your country or region. 

When you request to deactivate your account, you receive a unique alphanumeric access code. Make sure that you keep this access code in a safe place – you must have it to reactivate your account. 

After we verify that you are the account holder making the request, we deactivate your account.

Can I reactivate my account?

Yes. If you request account deactivation, you'll receive a unique alphanumeric access code. When you're ready to reactivate your Apple ID, contact Apple Support, provide your access code and we’ll help you reactivate your account. If you lose this code, we won't be able to help reactivate your account. 

3.

I have forgotten my password and therefore I cannot change my information or buy any apps. Is there a way of changing my Apple ID email address?

If you stil have / know that old Apple ID, check your Apple ID via your email box, see this Apple article: If you forgot your Apple ID

If you forgot your Apple ID email address or phone number - Apple Support                  

OR see -> Having trouble signing in?

https://iforgot.apple.com/password/verify/appleid

Try this -> If you can't connect or sign in to iCloud

If you can't connect or sign in to iCloud - Apple Support

See also -> Contact Apple for help with Apple ID account security

Contact Apple for help with Apple ID account security - Apple Support

BTW: You are sign in here .  .  .  with your Apple ID & Password.

Your Apple ID is the personal account you use with all Apple products and services. It includes the email address and password you use to sign in, as well as the contact, payment, and security details that you use with Apple.

You can’t merge multiple Apple ID accounts.