Yes, that white fuzzy scale bug is called cochineal, and is used as a dye for many things--including a lot of foods, such as "ruby-red grapefruit juice."
Regarding prickly pear, if you just want to make jelly, an easy way to juice them is line a colander with a couple of paper towels (or I suppose coffee filters would work), fill it with "tunas," and freeze them. The ice breaks the cell walls, so when you thaw them (over a bowl) they kiind of disintegrate and the juice seeps through the paper, leaving the little spines (glochids), seeds, and fruit sludge behind.