"Do you speak Arabic or Persian?"
Translation:Sen Arapça veya Farsça biliyor musun?
This is actually a social difference. I guess in English speaking countries people occasionally either speak a language fluently or don't speak that language at all. Since English is a wide-spread accepted language, they are actually more reluctant to learn languages. I am not saying they don't learn foreign languages but there has always been a difference between our approaches to learning second languages. That's why they use 'to speak a language' more often than 'to know a language'.
However, it's a different story in Turkey. We usually don't have such a diverse ethnic culture as English speaking nations do and we also strive to learn popular European languages which are very hard and different to us to reach a level of fluency. We usually study and learn but most of the time fail to speak them. That's why we use 'bilmek' more frequently than English speakers. However we also use konuşmak (to speak) for fluent or native level use of languages especially for ones such as Kurdish and Arabic.
Veya is just a straight choice between two choices. Whereas ya da is an 'either/or' = 'ya/ya da' situation. For example 'either(ya) you will learn or (ya da) I will punish you'. Imagine being Turkish and learning 'one way or the other'. That statement just don't cut the mustard :).