I hope I can help on the geography. Buckley didn't officially exist until 1897 when the parish of Buckley (Mold) was carved out of Mold Rural parish. However, there was also the parish of Buckley (Hawarden) which was created out of Hawarden parish then in Chester district. The whole of Buckley was donated to that district in 1902, but the Flintshire parishes were used to create Hawarden reg district the next year.
From old maps it seems that the boundary between the two Buckley parishes (and hence between Mold and Hawarden earlier) ran a little north of Mold Road in the west and then crossed the future A549 to run somewhat south of Chester Road in the east.
Buckley Square I remember from its post office which was to the west near Stanley Road and the pub (Hope and Anchor?) and west of Bistre Church, but it's possible that some of the Buckley Square area came under Hawarden. The boundary with Argoed must have been unofficial in those days but nowadays is the top of Pren Hill a little further west again.
There is a modern ward of Argoed consisting of Mynydd Isa, Bryn-y-Baal and New Brighton but that may not correspond to the original Argoed. The area was then much more rural. The nearest colliery would be in Buckley itself, I think - there was one at the Elm, though another at the Laurel in Sychtyn and others at Padeswood and Mold.