I believe I have this set up properly now however, I have some of questions.
1. How do I assign an external user to a specific employee?
Create a new Approval Hierarchy for a specific Employee as a Approver. Follow below steps for Creation.
Go to Approvals click on Add and follow the steps in numerical order as shown in screenshot.
Now Specific Employee Approvals will be setted and select this approval type in Timesheet Approval Type in project page.
2. Will the external user receive an email stating that there is a timesheet awaiting their approval?
Yes, once the timesheet is submitted a mail will be triggered to external user.