As for insurance, you can take out insurance in any insurance company without any problem.
3. The warranty can only be carried out in the 4s shop where you originally purchased the vehicle. This can't be moved to Shenyang, because you didn't buy the car in Shenyang, and the dealer in Shenyang didn't make money for you, so you can't provide warranty.
If your car runs in Shenyang, there is no problem. If you have been running in Beijing for many years, I suggest you apply for a Beijing license directly.