How do I create a role-specific registration page? I would like to create a "hidden" registration page that I can send to our wholesale customers in order to sign up as dealers, instead of standard authenticated users.

As our dealers have access to wholesale pricing, I will require that this type of user be approved by the admin. 

I will need to add a few new fields that I would only like to be shown on this dealer-specific registration page (vs. std), e.g. company, company address, POC. Do I create a new template for this form?

How can I add a Honeypot field to this form?
I suggest you to try the Multiple Registration module (https://www.drupal.org/project/multiple_registration), since this is precisely what it does "adds ability to create role-specific registration pages."

And as for the need to add the "admin approval" functionality, too, for specific user roles on your site, I would recommend you the Registration Role with Approval module (https://www.drupal.org/project/registration_role_with_approval)

Also, see if you will find this post of any help: https://www.optasy.com/blog/how-create-role-specific-user-registration-forms-drupal

Good luck!