Reminds me of Microsoft Wallet. First it was introduced in Internet Explorer (client-side) then shifted to web-side Microsoft Passport (now known as Windows Live ID). A really failed attempt or you can say never catch on.
Looks like Google Checkout is version 2.0 (as of Web 2.0) of Microsoft Wallet. Like Microsoft Office (client-side) and Google Apps (web-side).
I put Credit-Card information once in Google Checkout, then I don't have to put information again to purchase any item that support Google Checkout. Great, but I don't enter credit card online information everyday, maybe once a month.
These kind of "automatically-use-credit-card-information-on-disk-file" services are great for people who use credit-card with very high frequency (weekly, daily or more often).
Last night, I was very sleepy and couldn't find any clear help link in Google Checkout. Sleep makes me that stupid that I didn't even did Google search for help on Google Checkout. I am adding answer to my own questions to help other Wiredians
By the way, I can't find to make sure that Google doesn't send information about my credit-card to third party websites from which I purchase item.
Google does share some information (telephone number, address etc.) with third-party but does not give out credit card number to third-party
If I purchase an item that is on third-party website then does Google pay on my behave without releasing any information of my credit-card to third party?
I am still not 100% sure but looks like Google pay on your behave
What will be on my credit-card's monthly report (Google Checkout or third-party's name)?
GOOGLE*Seller's name will appear on credit-card's monthly report
For more details http://checkout.google.com/support/
It's good thing but it will be much better if they start services like PayPal. By the way, I read on some web that Google Checkout was (maybe still is) ban on eBay. http://auctionbytes.com/cab/abn/y06/m07/i06/s02