How can I get the transaction history of a bitcoin address? Lets say that I have a bitcoin address that is not owned by me. Is it possible to get that address's full transaction history (send/receive addresses and amount), and if the owner bought bit coins using a credit card will I be able to see that and possibly the card number? If not, what can I see with just a random bitcoin address, and who can see that credit card number?
Is it possible to get that address's full transaction history (send/receive addresses and amount)

Yes, all that information is in the public blockchain.
type the address into any blockchain explorer

if the owner bought bit coins using a credit card will I be able to see that and possibly the card number

No. That information is not public. It isn't really part of Bitcoin - not the network protocol, the blockchain or the reference software.

who can see that credit card number?

The merchant involved may, or their payment processor. But this part of your question is absolutely nothing to do with Bitcoin.