1. Twice a year, divided into higher education (university) and ordinary (middle school, primary school, preschool).
The first registration is at the end of February and the beginning of March every year.
The second registration is around September 10.
The registered permanent residence is not in Shenyang, so you can apply as long as you study or work in Shenyang.
Specifically, you can go to China Education Learning Network, which is very detailed. Moreover, that website has a lot of real review materials for the teacher qualification examination that can be downloaded for free, and the online courses they do are also quite good and can be listened to for free. Go and have a look.