Let me attempt to answer these questions.

1. The email is sent during invoice register update (one email per invoice).  It has a link to a Paya payment page which shows the invoice details.  The customer can pay the invoice there.  I don't think that page can be embedded to your website.

2. The email and the payment page can be customized with your company name and logo.  You need to ask Paya to show you how.

3. The customer will get an email.  They can also log into a customer portal to see their invoices and payments.

4. You get an email and  you can log into the merchant portal to see the invoices and payments.

5. The customer can only pay one invoice at a time because Sage 100 imports the payment records into cash receipts.  Sage 100 needs to know which invoice was paid.

6. Payment records are imported into cash receipts.  There is an Import button on the Cash Receipts Entry - Deposit screen.  After the records are imported, you print and update the cash receipts register as normal.   If you are asking about how you receive the actual money,  you need to ask Paya.

Thank you for the information! Is there a demo site or video to show how this works?

Sorry for the late reply.  This is the only demo I found:

https://www.sage.com/en-us/cp/sage100cloudlearningseries/

There is a link to a recording under "The road ahead for Sage 100cloud version 2020.0 and beyond".  The eInvoicing demo starts at 30:50.

Has anything changed with this program over the past couple of years? Like the product but not ideal to pay one invoice at a time or email one invoice at a time.

A separate email is still sent per invoice however multiple invoices can be paid through the Customer Portal. 

Has anyone been successful in customizing the email that is initially sent to the customer?  The email looks very "spammy'.  I called customer suppport a few times and they are unable to tell me where I can customzie this.   I don't feel comfortable sending this email to my customers.  Here is a screenshot of what was receive when I did a test: