Well, with portrait mode, as you know, you have to be at the right distance to achieve the effect, and it has a pretty good guide to keep you in the right place to take a photo where the subject is focused. But I have found it is easier to get an unfocused photo in this mode, only because you have to keep the subject at a specific distance, and there are other prominent objects at the same or close to the same distance, I think it requires some finesse.
I also have photos that were in the photo mode that have an unfocused background. I think for the regular photos it depends on how close you are to your subject and how much depth of field you have in the background. I even have photos from my iPhone 4 and 5s that have this effect sometimes 🙂
But if tapping the face doesn't focus a normal photo in, then it sounds like you may have some issues with the camera. Not sure if what is showing in the lens area would affect that since it is below the actual lens, but it would be best for you to have Apple look at it and explain what the heck that is....
Best of luck,
GB