Security

This depends largely if the purchase is done online or at a brick and mortar store.  Brick and mortar, only a driver's license is needed to verify you are the cardholder.  Most of the time you don't even need to provide that so long as your card is signed. 

Online, however, they need your shipping address, billing address as stated on your credit card, 3 digit number on back of credit card.  So they do more checking online to verify the card and the cardholder is the same. 

I'm not sure what you mean by record information from your card for their own purposes, but generally the answer is no.  They should use your card ONLY to process the transaction.  That's it.  They can, however, use your personal information (name, address, email, etc) to send you marketing information within the constraints of the law.