The so called "third eyelid" is called a haw. Google it and you will know all about it. I have a great dane and when he sleep his bottom eyelid droops so you can see that it covers the front of the eyeball.
Dogs have a normal eyelid like a human which shuts every so often, but they have a very thin white one under the normal eyelid, this only closes when the dog is full asleep. That is why if you wake them up suddenly you can quickly see a white bit on their eyes. So they have 2 not 3. Hope it helps.
No!Dogs have as many eyelids as human's do.
No they only have two because they have two eyes.