Creating new users with Commerce & Rules: ERROR
During anonymous checkout, an email address is collected from the 'Account information' pane to create a new user (or append the order to an existing user).

You should be able to hook into the form on the 'Account information' pane and add your required fields. You will probably have to modify the rule (Create a new account for an anonymous order) to send along the extra fields for creating a new user with the required fields - when marked required, custom fields added to the user are added to the Create Entity action for user as well.

You can populate these fields using existing variables, or fields added to the Commerce Order or Commerce Billing Profile, or create your own variables (eg via hook_token_info_alter() to make variables available through the commerce_order).