The microvilli are no more than about 100 microns in length and perhaps 10 microns in diameter, just barely visible in a good light microscope. The goblet cells have a few scanty microvilli, but they aren't heavily covered with them the way the enterocytes are. The cells rest on a basal lamina, which you may be able to make out in this image as a bright line underneath the cells. They sit over the lamina propria , the loose collagenous CT, filled with cells, that constitutes the core of each villus. Constant roliferation of enterocytes and goblet cells in the deepest portion of the crypts replaces the vast numbers shed at the apex of each villus.
New cells arise by mitosis in the deep crypts and migrate up the sides of the villi to the tips.
Goblet cells were at one time thought to be long-lived, but this is open to doubt. The goblet cells on the villi are exposed to the fully digestive action of the lumenal enzymes.