Invoice notes are visible on the invoice PDF.
Internal notes are only visible to your internal team in the invoice settings.

Yes. Click the customize icon beside Invoice Notes to edit them. Your changes will appear in the invoice PDF and will be seen by your customer.
When creating an invoice, if you select a contact that has default invoice notes filled in, those will automatically be applied to the new invoice.
For more information about default invoice notes for contacts, refer to What is the "invoice notes" section for a contact?