How to associate separate email notifications to drop-down items?

We have a system set up using another form service where, when a user selects one of many franchises in a drop-down selection tab then presses submit, three things happen: (1) the dealer at the selected franchise is notified, (2) the corporate company is notified, and (3) the user receives a confirmation email showing the info they entered along with some other info.  Is something like this possible via Jot Form?

Yes, this can be achieved through Conditional logic and Setting up email notifications

Please refer to the guide below that can help you with setting up conditions for emails.

https://www.jotform.com/help/167-How-to-Send-Email-Based-on-User-s-Answer

To explain it better with example, lets say, I have a condition that if the Name field is filled, then the autoresponder will be sent to the email address.

To set up autoresponder please refer https://www.jotform.com/help/26-Setting-Up-an-Autoresponder-Email

Setting up Autoresponder will allow to send email to the user filling the form with the information filled in by him or any custom information that you wish to send after the form is submitted.

Hope this helps.