I don't know a lot about this in the big picture, but I'd like to recount something personal, if you'll bear with me.
I have a chronic, incurable illness. I've had it since I was about 15 (so nearly 15 years now). Doctors, medications, surgeries ... they have all been helpful, but there are no cures.
I reached a point in my life not long ago, that I started looking "outside the box" for ways to help myself. Would I like a cure? Of course, but I'm not banking on finding one. However - I have found some alternative methods that have provided more symptom relief than medications.
Someone (I'm not sure who) mentioned chakra meditation - I do regular meditation, with a focus on points of pain. When I do this, I imagine the places inside my body that hurt covered with a whiteness. While I breathe in and out, the energy is directed to those places, and there is a warmth to it. Since it isn't a permanent cure, it's probably not appropriate to call it "healing," but considering it is often more powerful than the Rx medications I have for pain, it's certainly something.
As for the healing power of prayer, I do believe in that. When I had my last surgery (2.5 years ago), a friend in another city was praying for me on and off a lot in those first couple of days, as those days are the worst for pain and discomfort. On and off, I would feel that same warmth in my body, and I would feel my heart rate slow down to a comfortable, relaxed pace. I was allergic to the pain meds they gave me in the recovery room, so I was actually NOT taking a single thing for pain, even that first night, because I was afraid of another reaction. So through the suffering and agony, I could feel this warmth and this comfort, and I didn't actually know that my friend was praying for me at that moment. It was later on that she told me that, and it was incredible.
It's just my own story, and of course anecdotal evidence is not proof of anything, but I wanted to share that anyway.
As for why some people get healed and some don't - to me, that's like asking why some suffer in the first place, while some don't. It's a question without a real answer. I've been sick for 15 years, and have had moments of real bitterness and anger - why me?! I'm not bitter or angry anymore (mostly) but I still don't have an answer.
I'm not sure if I believe a person can lay their hands on someone and cure them of a brain injury or anything like that - and if they can, that's God's work, not the person laying hands. However, after what I experienced post-surgery, it can't hurt.