Yes, it is called Pricing Group in Flex Catering, which allows for price tiering for specific customers or groups.
Yes, you can send their account link. Your client can log in to their account and make the payment by credit card.
As payment methods we have integrated PayPal and various credit card portals (Stripe, Square, Adyen, eWAY, SecurePay, Commbank Simplify & Authorize.net). We can integrate any credit card merchant at a cost. You can also allow your customers to pay by invoice (bank transfer or cash).
Yes, you can create a new customer in the add order process.