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The answer to your question, "do people buying from my page have to have a paypal account?" would be no they do not have to have a PayPal account to make purchase on your website. You can set up Website Payments Standard or Website Payments Pro which allows your customers to either log into their PayPal account or pay using a credit card. If you still have questions here is more information on how PayPal works.
No. However we have found its a good idea to tell your customers very clearly that they don't have have a PP account at several places on your cart and website before they are handed over to the PP payments page since PP doesn't make it as clear. as would be nice.