How do I add the individual item line totals for a grand total?

I'm trying to have the total automatically calculated from the individual line items to be reimbursed in the table prior.

On this same form - is it possible to have a field where someone can sign/authorize after the form is submitted?

Thanks! 

Yes, it is possible to calculate a total based on inputs in the matrix field (Items to be reimbursed), please check this guide that will help you to do it: https://www.jotform.com/help/343-How-to-Perform-Form-Calculation-in-the-Matrix-Field 

Regarding to your second form, it is possible with conditions, you could first submit the form to the desired recipient so the submission is reviewed with the edit link, while editing the submission you could show the needed fields included a signature widget. 

Here're the guides that will help you to achieve this. 

This widget will help you to know when the submission is being edited: https://widgets.jotform.com/widget/get_form_page_url 

This will help you with conditions to show or hide fields based on the widget above, which will allow you to know if the parameter "edit" has been passed in the URL: https://www.jotform.com/help/316-How-to-Show-or-Hide-Fields-Base-on-User-s-Answer 

The condition should be similar to this one: 

Here you will find some widgets that will allow you to capture signatures in your form: https://widgets.jotform.com/search/signature 

This guide will help you to add the widgets to your form: https://www.jotform.com/help/252-How-to-Add-a-Widget-to-your-Form 

Hope this helps.