I will try to answer some of your questions based on my experiences
1. Most likely the 2017 slot for parent sponsorship will open sometimes January 03, 2017 but please double check the website for the exact date. I would suggest submitting the application as soon as possible when they open the slots as it going to be filled very quickly if your sponsor can submit it the first day of opening the better. Like last year the cap reached after 5 days i think.
2. Yes you will need to obtain a police clearance for each country that you have lived for more than 6 months.
3. As long as the sponsor is a PR or Citizen he/she can apply for sponsorship provided that he/she is qualified. I believe one of the requirements is too meet the income threshold for the last 3 years preceding the submission of the application.
4. Medical insurance is not a requirement for PR application but Regardless if you are applying for PR, if you are staying in canada as a visitor you will have to have a medical insurance renewed each year. as you wiil not be covered with the health system of canada if you are a visitor status holder.
Hope i helped a bit good luck