Is my gum healing properly? Why are the stitches coming out before time! (photos)

Your photos are not very clear but I would guess they are gut sutures which tend to dissolve pretty quickly. If your dentist extracted a tooth, he likely used gut sutures to keep the tissues together. If there was no bone graft used, you have nothing to worry about and this will heal. If you are concerned, call your dentist and go see him for peace of mind. You should be fine. 

Thank you for your question. When tissue heals, swelling goes down and sutures can get loose after 5-7 days. I would not worry about it, but for the piece of mind, call you doctor and let him check and make sure.

Different types of sutures dissolve at different times.  If you were told the suture should hold for two weeks then that can mean that the knot came undone or that something caused the suture material to loosen up sooner.  In itself it is not a big deal as long as the wound is closing.  I would have the doctor assess the area to make sure