Is it possible to just send an e-mail to the approver for each submission?

Is it possible to just send an e-mail to the approver for each submitted form with a link to the form and allowing the approver to approval or reject the form? Also, allowing the approver the capability of telling the submitter why their request was rejected.

This is the solution I am looking for.

You could do that by editing submissions (https://www.jotform.com/help/325-How-to-Edit-Submissions-Made-on-Your-Forms) and you could add two more fields to your form:

Add Get Form Page URL widget:

And make a condition that will reveal those fields:

When you edit the submission those hidden fields will be shown so you can approve and explain why.

Also, you should enable "Send on Edit" in Autoresponder:

So your users will receive an Autoresponder when you edit a submission.

Let us know if you have any further questions.

Thank you!