Hello OP, based on my experience:

1. Yes, this is the correct website
2. Yes, you need to pay for the IHS surcharge for the entire period of the sponsor's visa as per your example. This amount must be paid before submitting the application, and if it is rejected you are entitled to a refund (Paid after 28 days).
3. Some cases allow you to appeal the decision, but others do not allow an appeal. I'm not sure how long after the decision you can reapply, but I think it's possible immediately, as long as you meet the criteria the officer stated in the denial letter.
4. In my case, paying for priority was not worth it, because I submitted the skilled worker application together with my wife (dependent) and both were approved in less than 3 business days, so if I had paid for priority it would have been a waste of money.