Does this site use European Spanish or Latin American Spanish
We travel to Spain and know there are differences between the South American Spanish and European Spanish. In fact I understand there is: Castellano; Gallego; Catalan/Valenciano and Euskera.
using this site how do we know which of the four above applies?
There are some serious differences in pronunciation between the Spanish of Spain and the Spanish of South America, but if you speak one, you will be understood by those who speak the other. In fact, we recently had an exercise on this site comparing native speakers from both areas. It's similar to the difference between the British and the US flavors of English.
I can't speak for the lessons and flashcards, but you don't have to worry about distinguishing between Gallego, Catalan, and Euskera on this site. They are different languages from Spanish. In fact, Euskera is completely different altogether - the other two are similar to Spanish but you'll know Euskera if you ever run into it!
As for the forums, there's a great mix of native-speakers and fellow learners from all over if you ever have doubts about regional usage.
The Spanish language spoken all over the world was first known as Castellano in Spain because it is originated in Castilla, one of the several kingdoms that were created in the Spanish peninsula during the retreat of the Muslims.
It took the name "Español" after the unification of Spain and the foundation of the Spanish Empire.