My FM db schema is attached. Please refer to it and see if it makes sense. Specifically, does my relationship around Appointments, LineItem and Payment make sense? In addition, one of the things I would like to do is create invoices. I'm a little confused on whether or not I need a separate Invoice table for this?

Your Appointments table looks like it is essentially a "work order" table. Some systems use the work order as the invoice table too, just using a different layout, and maybe a field to indicate whether the status is invoiced. You might also want to have a field in line items to flag whether the line item should appear on the invoice or not. There's no one right way to do it, it depends on your specific needs.