Must my customers have an account with Paypal to pay me with Paypal?
No, when a customer pays you with Paypal, he doesnt need a Paypal account. He only needs a credit card.
To help you understand the payment process by Paypal, see the questions in the following FAQ : ''How to accept credit cards?'' and ''How to accept credit cards WITH Paypal ?''. These two questions are in the category ''Modes of payment: credit cards, Paypal and others'' of the FAQ.