I have already integrated Google checkout with Magento basic website,
when someone buy a product, my google checkout seller account is getting the payment and getting e-mail confirmation from Google checkout too.
But I am not getting the order in my magneto admin: Sales > Orders area.
I haven't used it with magento, but I assume you need to specify a callback url in your magento installation.
In the Google Merchant center, go to settings, then integration, and there is a text box "API callback URL". This should be whatever url that magento uses for GCO callbacks. Without this part, your website would have no record of a sale being finalized in GCO.
If this is already filled in, go to the Tools and then Integration console in your google merchant center and see if there are any reported errors.