The basilisk is a reptile of Greek legend known as the king of the serpents. It reputedly had the power to cause death with a single glance.
Mediaeval European portrayals of basilisks (as pictured) added elements of the cockerel. Basilisks were said to derive from serpents' eggs hatched by cockerels.
According to the law of the time, drinking oneself to death was tantamount to committing suicide, so Heathcliff is right to suggest the cross-roads for Hindley's grave. However, if Hindley were officially declared to have committed suicide, his property would be claimed by the Crown, and Heathcliff would be unable to gain possession of it. Hence Heathcliff does not press the point, but allows Nelly to perform a proper burial to safeguard the property.
Ponden Kirk is believed to be the inspiration for Penistone Craggs, the place where Cathy and Heathcliff go to escape Hindley and the place that so captures the imagination of young Catherine. Ponden Kirk has a natural hole in its base that corresponds to the Fairy Cave Cathy speaks of.
The name Penistone likely comes from nearby Penistone Hill.
Carriages in the 19th century were horse-drawn and usually available only to members of the upper classes. There were several different types of carriage available, including the Barouche, Curricle, Landau and Phaeton.