Might not be fast enough, but I'll have a go...
AFAIK, the first pit head baths were introduced by a Lancashire firm called Fletcher-Burrows, just before WW1, possibly at Gibfield colliery.
It took many more years before PHB's were widespread, some were well after nationalisation in 1947. At Lepton Edge Colliery, baths didn't appear until c1958. This pit closed in 1964, so the baths were only 6 or 7 years old.
Whenever my dad was thinking of moving to a new pit, "Do they have baths?" was always a consideration.
Not sure what you mean by "air engines that drove the coal out", so I'll leave that.
Most of the holes drilled at the coal face would be in the days of "hand getting". The coal was first undercut by a man with a small pick (later by a coal cutter machine), then a series of holes drilled close to the roof. After packing with explosive the shots were fired & the coal brought down. In NCB mines, this process was carried on into the 1970's, possibly later.
Hope this helps...
Edit to say, just checked the album for "Gibfield Colliery" & the first PHB's were at this pit...
Regards, John...
Huddersfield, best value for money in the country, spend a day there & it'll feel like a week........