How do I request SMS verification on a device with iOS 8?

See if anything here helps.  If necessary, you can use account recovery as explained in the link at bottom of the article.

Verification code - how to get one and sign in with two-factor authentication.   *

From the article below. If it has been on longer than 2 weeks, you can't turn it off. 

Can I turn off two-factor authentication after I’ve turned it on?

If you already use two-factor authentication, you can no longer turn it off. Certain features in the latest versions of iOS and macOS require this extra level of security, which is designed to protect your information. If you recently updated your account, however, you can unenroll for a period of two weeks. Just open your enrollment confirmation email and click the link to return to your previous security settings. Keep in mind, this makes your account less secure and means that you can't use features that require a higher level of security.

Apple ID -Two-factor authentication.   *

Right now I don't have any Apple devices.

Why do you need the verification for?

Is there a way to request a SMS verification or to turn off 2FA?

If you already use two-factor authentication, you can no longer turn it off. Certain features in the latest versions of iOS and macOS require this extra level of security, which is designed to protect your information.