Is it normal for a dental implant to be exposed after surgery? Or do I need extra stitching? (photos)

If healing screws were used to allow the gum line to form, then yes, it is normal. From the photos you submitted it appears that they are partially exposed and may require removal of gingiva prior to restoration with crowns. Of course, you should see your dentist for an evaluation since the images are not diagnostic.

Its hard to tell from the photos if you have what is called a healing abutment or a cover screw. If the doctor placed a cover screw, the gums would be stitched over the top and you would have to wait a few months before it can be "uncovered." If there is a healing abutment, this is meant to be seen during the healing process and starts to form the shape of the gums. If the doctor did place a cover screw and the implant was supposed to be submerged, then I would have someone look at it because you might have lost some bone on the implant.