H1 visa for canadian PR and citizen

I am H1 4th year in US but did not get GC yet. Thinking about attending school in US, please help me out these questions
If I immigrate Canada and get PR, then attend school in US based on Canadian PR, or attend school in US based on H1 visa

(1)Can I apply canadian citizenship during my studying in US school?
(2)If I use H1 visa attending school, it is very likely my whole 6-year H1 will be gone when I graduate from the US school, can I apply H1 again based on canadian PR or citizenship at that time? In another word, is it true that one person could only be granted H1 visa for 6 years in the life no matter whether I am a china citizen then becoming a canadian citizen? Thank you very much for your response!