A minor note: The eyelids should not cast shadows on the eye.
Here is the way I like to do it without that gap.
First I select my eyeball and I make it live by hitting the magnet button. If you cant find the magnet just write "MakeLive;".
Then just select the vertixes you would like to edit and move them using the circle in the move tool. I usually move the vertixes one at a time.
There seem to be some things that should be changed regarding anatomy but a picture of a human explains that better then me.