Canada to Shangahi to Hong kong to Canada

I am a Canadian planning to fly to Shanghai from Canada for 6 days then fly to Hong kong for a week and then fly back to Canada. Can I use the 144 transit free visa to Shanghai? I am also thinking to fly to Beijing for 3 days when I am in Hong Kong. Can I use the 72 hours transit free if I plan to fly back to Hong Kong from Beijing? And then fly back to Canada.

Thanks.