Unsubscribe module issue
Using module Unsubscribe
About the &quot;not appearing in fields of user register form&quot; in the question: it seems to me that the unsubscribe module might just be working as designed, and implemented. From its project page (I added some markup here):

The module design is very basic. When a user unsubscribes, they are added to an &quot;unsubscribe list,&quot; which is stored in the database. Whenever Drupal sends mail, the unsubscribe module will check to see if the recipient is on the unsubscribe list. If so, the email is blocked. You can exempt specific modules from this blocking via the configuration page. You can also use hooks to alter exemptions, or override the blocking.
Emails sent by the system and user modules are currently exempt by default.

From the question it is not clear to me what you have done regarding the &quot;exempts&quot; (on the module's configuration page). If nothing yet, then that might be the explanation for why it is not appearing on the user register form, no?
Using some other module
As per your &quot;any other module that provides a similar function/feature&quot;: it appears to me that the Rules module should be worth considering, possibly combined with the Message module.
If you're not familiar enough with these 2 modules, then I suggest to review this great introduction to the Rules module: Rules for admin notifications, Part 1: New user registrations. Maybe also the related Rules for admin notifications, Part 2: New comments and content.