Emily Brontё had developed an impressive knowledge of the property law of the late 18th century, much of which had changed by the time of her writing.
It was commonly believed that somebody lying on a pillow stuffed with pigeon feathers could not die, as the soul would be prevented from leaving the body. According to the Encyclopaedia of Superstitions 1949 (E. Radford, M. Radford) there have been 'instances where a bag of pigeon feathers has been deliberately put under a dying person's head for a pillow to "hold him back" until an expected relative could arrive'.
The feathers are not red, so Cathy is presumably asking Nelly to check for blood on them.
Lattice windows feature heavily in the book, and are repeatedly mentioned in connection with the Wuthering Heights house.
Large sheets of glass were expensive. It was cheaper to have windows made up of many tiny panes joined together with lead. Today they are a much-loved feature of many English country cottages and other period buildings.
Heather grows abundantly on the Yorkshire moors and its bright purple hue is one feature which makes this landscape so stunning. Catherine longs for it when she is bedbound at Thrushcross Grange, as a sweet reminder of freedom and her childhood spent roaming the moors with Heathcliff.