It's essentially right there in front of you, although it's a bit covered by the lungs, especially the left one, so you need to push those aside. Look at any anatomy book. There's always a front view of the open chest with the heart and lungs in position, although anatomy books usually show the organs with the whole chest plate -- the front portions of the ribs and sternum -- removed so you can see a bit better. The only time that is done is during an autopsy, in which case the ribs are cut all the way around the sides using something like a hedge clipper.
It heals, but any bone fracture (which is really what sawing the sternum in half is) needs to have the edges of the bones brought together and held in position to heal properly. That's why we put a cast around a broken arm -- to hold the edges together until they heal. Sometimes we need to use plates or screws to hold the edges together. This is the same situation: the wires that George mentions bring the edges of the sternum together and hold them there. By a couple of weeks later the sternum is stable and the wires don't serve any purpose, although we leave them there because it's too much of a hassle to pull them out -- it would take another operation to do that.
It would be tough. It takes 7 years after medical school to mint a cardiothoracic surgeon. As George mentions, what you're considering for your plot requires some pretty major stuff. On the other hand, fiction is fiction, so I don't think it's totally impossible. Maybe you could give your character some previous experience? Maybe working with animals? The ranchers around where I live are pretty good practical surgeons.
