It looks to me like you are hitting the ball low and behind you a bit which is effecting your power. I would also say that your timing looks a bit off as you seem to be finishing your rotation (at least with your feet) before you contact and you are not pushing up through the ball but instead kind of stepping down. That is an uninformed opinion though. This seems like a useful exercise and I am definitely going to buy a video camera for my serve.
As to shoulder pain, I have had this issue since I was about your age and it never went away. I got over it using Advil at the time. I am definitely not recommending this as an option though. What did seem to improve things for me was doing military press to strengthen the shoulder muscles.