sclera
I think it is called a 'Nictating Membrane'.
Yes, when the eyelids are closed, they cover the entire eyeball including the posterior portion. This helps protect the eye from external elements such as dust and debris.
The outer transparent protective cover of the eyeball is the cornea. It helps protect the eye and refracts light to focus it on the retina at the back of the eye.
The eyeball is a directional adjustable fitting on the water return on your pool wall. Its called that as it looks like an eyeball.
Exophthalmos
back eye
The Iris.
sclera
Sclera
intraocular fluid
schlera choroid
They don't pierce eyeballs.