It's time for a new vet
No need to take your turtle to the vets as he'she is just fine
At some point in time your turtle had shellrot in that area and some of the bone died (the white bits you have pictures of). When the dead scute material on top of the dead bone came off it made it easy for the bone to come off. Everything that I see says it's all long healed. The black bit is new scute material (put down under the dead bone) on top of live bone.
If you can get a picture of the side of the head (with the head out), I can tell you what kind of map turtle you have.
Danny