There is definitely a hole there, no doubt about it. Right over/into the sinus. The bird obviously has multiple issues going on. My best guess is that this started as a simple eye infection. Especially during the winter when they don't have regular access to swimming water, ducks will get eye infections. Sometimes it is not even an infection per se, rather it is an irritation around the eye that can lead to some really nasty looking matting and discharge. Runners are particularly prone to this. I just had one of my Runners get a really bad case of this earlier in the week (we have raised Runners for 20+ years). I was sure the bird was going to need an antibiotic, he looked so bad and this was a bird that had access to a dish he could have almost submerged his whole body in. We separated him and I have been toting fresh water out to him in his own private swimming pool constantly and within just a few days, he is back to normal.
When I hear you say you are going to clean around or remove the scab, I literally cringe (because I know from my own experience, how easy it is to tear the skin). DO NOT do that. That looks like part of, if not the main, problem the bird has as it is (not that this was a result of something you did, it could have easily have been another bird picking at it). I am guessing that this started as an eye infection and moved to the sinus because the missing patch of skin is literally right over the sinus. When a duck gets a sinus infection, you will see a swollen bump right there. In an attempt to clean the area, you can quite easily tear open the skin (which pretty clearly looks like has happened). I am not surprised that you see new growth underneath what appears to be a scab. That is normal. Ducks are very resilient and tissue can heal very quickly. Really though, if at all possible, I would see a vet. Definitely continue keeping her isolated and give her WATER, WATER, and more WATER. Let her keep the area clear by swimming. Do not put her back out and do not go picking at the scab. Continue with the fresh swimming water and an antibiotic eye cream at a minimum. Whatever gooey stuff is there will come off as she is able to swim in fresh water (that is almost certainly why you are seeing improvement).
The issue of the bare patch on the back is an entirely different issue. Obviously, you can't keep the bird with a turkey that is mating her. Runners are very light weight ducks. A turkey is not. From the looks of her, I am kind of surprised he hasn't broken her back already. If you keep them together, you will almost certainly find her dead at some point (probably sooner than later). It is unfortunate, but it is reality. I know it is a hassle in a mixed flock to keep them separated, but in a case like this there is really not much choice. Good Luck! I think she has a good chance of rebounding as long as you keep up the good work with the swimming water, etc...
