Possible, paid but not for 2-step - just for custom domain.

tl;dr;

Usage of Google mail servers with custom domain requires Google Apps for Bussiness, formerly knowned just as Google Apps.

Quoting from Google Apps Help Center

As of December 6, 2012, Google no longer offers new accounts for the free edition of Google Apps

To enable two step-authentication go to control panel of your domain:

• Security -> Basic Settings -> Two-step verification
• Click to checkbox Allow users to turn on 2-step verification

There's no additional fee for two step verification.

Possible, paid but not for 2-step - just for custom domain.

tl;dr;

Usage of Google mail servers with custom domain requires Google Apps for Business, formerly knowned just as Google Apps.

Quoting from Google Apps Help Center

As of December 6, 2012, Google no longer offers new accounts for the free edition of Google Apps

To enable two step-authentication go to control panel of your domain:

• Security → Basic Settings → Two-step verification
• Click to checkbox Allow users to turn on 2-step verification

There's no additional fee for two step verification.