I'm afraid you won't find anything like a Delaware LLC in Europe. Our laws are just too diverse. In the US you have state laws and federal laws, but in Europe every country has their own laws. Especially things like consumer protection differ fromcountry to country, and can be a PITA.
As far as online payments go, you're stuck to either PayPal or the recently launched rocket internet stripe-clone called paymill. Haven't tried that out yet, though.