While you should probably double check with Support, my Chapters applied on both PC/NA and PC/EU (bought in NA). My DLC did not, as with all crown store purchases.
Yes, the chapters will apply to both - like the above said, the DLC does NOT.
Which, actually is horrific... having to spend 7,000 crowns on Summerset (which can equate to costing MORE than the chapter when it first comes out) is a HORRIBLE business model.