I would like to use in-app billing in my android application (instead of creation 2 versions of application - free and pro). If user paid, then additional options in Preferences should be available. My application synchronizes data with website (not my). Each time synchronization happens, I would like to check if user paid or not. How should I do it?
I think the easiest means for you would be to use Managed purchase. More on it is at http://developer.android.com/guide/market/billing/billing_admin.html#billing-purchase-type
The "manage by user account" purchase type is useful if you are selling items such as game levels or application features. These items are not transient and usually need to be restored whenever a user reinstalls your application, wipes the data on their device, or installs your application on a new device.
Update: website and API updated refer this now https://developer.android.com/google/play/billing/api.html