I have a site where people able to buy anything are already loged in. How do I collect from profile2 and apply this information in commerce billing automatically?
You're better to use Commerce Customer Profiles for that information.
Although "billing" is the default, you can add other groups of profile fields as types, e.g "Profile information" etc...
There's a module commerce_customer_profile_type_ui that helps creating new profile types, else you can do it in code via the API.