An example would be the recent movement in Catalonia that wants to secede from Spain. What is going on here and where/ when does it it stem from? Could it be a product of the Reconquista and merging of Castile and Aragon? The civil war?
I wish I knew. I bet r/askhistorians could give you some background though.
For a good answer, I'd suggest asking on http://history.stackexchange.com/
The culture divide was around long before the civil war, but more than that I can't say - my knowledge of Spanish history pretty much actually is limited to the civil war itself.
I dont know. When I visited Barcelona on a business trip I could make out an undercurrent of dissatisfaction among Catalans. The folks I worked with were a mix of local Catalans and Spaniards (I am using these terms merely to distinguish the local population from the rest of the country, not suggesting Catalans are not Spaniards). We hung out in the evenings and maybe one Sat. At one of the places we visited (I cant remember which) a Catalan in the group remarked "this place is our ground zero " (as in the 9/11 ground zero) but the non-Catalans sort of dismissed the comment. There was a little tension, enough that I thought it would be impolite to probe. From my brief "research" just post visit (more than 6 years ago) I suspect the tensions may have arisen because Catalan culture was suppressed during the reign of Franco. If I remember right the nationalist govt under Franco wanted to build a unifying national identity for Spain. Interestingly, classes at UPC are conducted in Catalan, Spanish, as well as English.
You can say Castilians as in there are three kinds of Spaniards; Castilians, Basques and Catalans.