Answers
The image will be fainter since you are cutting out half the light, but you will still get the whole image.
HERE A RAY DAIGRAM OF BOTH COVERED LENS AND NOT COVERED
This will probably be clearer if you draw out the rays. There are two rays from the top of the object to the image:
1) one that goes directly to the lens from the top parallel to the plane and goes through the focal point on the image side of the lens and forms an image.
2) one that goes diagonally to the bottom of the lens through the focal point on the object side of the lens and forms an image parallel to the plane on the other side