Can anterior shoulder instability cause nerve, tendon, muscle, shoulder blade problems?

Yes. This is very plausible. To be sure, and due to the complex nature of the shoulder, and evaluation by an orthopedist would determine the exact cause of your symptoms. Best of luck.
Yes. Due to the instability, the laxity of joint created by the instability can put a stretch on the nerves, tendons, etc., causing additional discomfort.