Does PayPal give your credit card number to the merchant when you use your credit card rather than your bank account for a purchase?

No, Paypal does not give your credit card number to the merchant when you use your credit card rather than your bank account for a purchase.

The merchant only gets a notification the payment was successful.

If you setup a recurring payment through paypal, the merchant will be able to charge you regularly through paypal without you initiating additional payments.

http://paymenttransactionsystems.com
http://merchantpos.net