I have a partial rotator cuff tear, that I never bothered to have repaired with surgery. The injury came from playing softball, about 15 years ago. Every shoulder injury is different. Not all rotator cuff injuries cause the same problems. Ranges of motion vary, etc. This makes it difficult to give good advice.
There are many useful exercises that can be done for a torn rotator cuff. Look some up or talk with others, or find a physical therapist to get advice from. I know a couple of physical therapists and they offer advice freely. The most useful exercise I do is the "empty can". Act as though you are holding a can drink and turn your wrist over as if you are pouring it out. Keep that position and with your arm straight, simply move your arm up and down slowly. Do this often and do a lot of reps. I do this exercise now with my lifting routine and use some weight. I find it works best for my shoulder if I use about a 45 degree angle from my body.
Lifting has helped me also. But, if you do this, be careful. Take it slow. For me, all exercises must be done with the elbow "in". Stay in front of your head with weight if you do shoulder presses. If you bench press, keep the elbows close to the body as is feasible. Elbows out puts pressure on the shoulder. Pullovers, pulldowns, chinups ... be careful with these and keep the elbows in.
If it hurts, do not do it!
What it has meant for my disc golf game is that thumbers are not an option. Forehand flicks are still doable for me, but without reachback. I really T-Rex my flicks. Kinda just wrist the thing out there. I cannot throw it far, but I use that shot a little.
I throw backhand mainly, and I find that I naturally do not extend my arm all the way when I throw. This is also probably a limiter in my distance. If I let my arm fly free on my throw, my shoulder is bothered. In some ways, my shoulder problem helps me work on things on my throw. I cannot strong arm it much. I have to focus on smoothness, and using my legs and body. I focus on my grip, keeping it passive until it is time to grip down. I can still focus on arm speed, as long as I don't strong arm it. I find it better for my shoulder to pull lower than my chest. Also, pointing my elbow at my target causes more shoulder pain for me. I drop the whole throwing setup a little and things do alright.
I am glad I can still play disc golf. I cannot play softball any longer.
I have known some people that recovered very well from surgery, and many who have not. I personally have never cared for the option of going under the knife for my shoulder.
You cannot HEAL a rotator cuff tear with exericise or therapy. You can work at it, build up the muscles around it, and gain more usefullness in many things. It sounds like you are on a good path already. Be patient with it.
I hope this has helped some.