I don't know if this helps put matters in context but between Whitby and Ruswarp the Whitby Gas works was situated almost under Larpool viaduct, pictures are in the 'Scarborough and Whitby Railway' and also both volumes of Martin Bairstow's 'Railways Around Whitby' its dilapidated remains are still there today the pools for the Gas Holders lie derelict while the whole site has a sinister air as some sort of home for abandoned boats lying at all angles although passing by on Tuesday the gates that accessed the railway from the private sidings are still there behind about 15ft of Gorse bushes and the major buildings still survive. The Gas Works would I imagine of been the only source in Whitby for 'Gas Water' as it was the only gas type plant in Whitby.
This link shows the plant in its prime http://www.friendsreunited.co.uk/whitby-the-viaduct/Memory/b01fa9b7-22d7-4c38-8c81-a02900c13046
Regarding the Flour and Bran to the best of my knowledge there were two large mills in Whitby and Ruswarp, I've never seen any reference to a goods yard at Ruswarp so assume traffic must of originated via Whitby, the mills at Ruswarp is still standing although is now flats having burned down twice while in use as a mill, I have it on good authority it was still milling in the early 1950's although the building dates from Georgian times. The other mill in Whitby was Union Mill situated adjacent to Pannett Park at the top of Chubb Hill, the building was pulled down after the war and made way for an Austin car dealership which lasted until the collapse of MG Rover the site has now been redeveloped and is again known as Union Mill the architects making the top look the dome of a Windmill while the bottom story has a pastiche pf the post war styling employed on the car dealership.
Ale and Empties is partly accounted of by Whitby having once been home to the 'Whitby and Scarborough Brewery' long since forgotten it worked out of the building on the harbour side that now serves as the 'Shafiq' clothes shop.
'Livestock' again I'm assuming Whitby was responsible for goods operations at Ruswarp as Ruswarp is home still to the local livestock market and even today what was once the livestock 'platform' at the back of the mart is still used for cattle pens separated from the railway by corrugated sheeting, as a farmer who uses the mart I can assure you very little else remains of the rail served facilities at the mart although if you pass by on the train the platform and siding space is still clearly visible.
Sorry if I've ramble on, hope this helps
Matt