I've never heard the term 'grain court' but it might have had something to do with the corn mill just across the road in Hyndburn Rd, then called Hagg Lane.
I too think that 'coaching inn' can be a term which takes in horse-drawn travel of any sort. It could have been the reason why a farrier /blacksmith was just around the corner from The Bull. I think that the name Bull Brtidge is still visible in the wall of the old bridge somewhere near the car park entrance, pout there buy the County Council c 1890, but it is likely, certainly possible, that there was a bridge there before that, and before a bridge there would be just a ford. It could be said that this was the very centre of Accrington in (say) 1700