Does the Ripple protocol allow listing an account's (address's) past transactions? If yes, is there a web site for this?
Yes, the Ripple protocol does allow you to list all past transactions performed. The most typical way would be to use the account_tx command. You can "page through" the data, retrieving a particular number of transactions per command, until you get to the first transaction.

I am not aware of a website where you can trace through an account's transaction history using GUI-style navigation, although the Ripple Charts Account Explorer will show you an account's transaction stream.