Awaiting Canadian residency, US student status soon to expire

Hello!
I have just applied for canadian residency after otaining my csq. I have heard that this process may take 6-8 months. Since I have not been able to include my police certificates (not issued at that time) and my OPT training in the US will expire in three months + 2 months grace period, I wonder:
1. Will my overstay in the US impact the issuance of the canadian paperwork? And if issued, will I be in trouble when I cross the US border to enter Canada?
2. If I succesfully land in Canada and become a permanent resident, will I be banned from entering the US for the next 10 years for overstaying my grace period?
3. Should I be proactive and apply for another degree program in the US, so I can maintain a legal status if I where to overstay my grace period? (This will cost me thousands of money and leaving the US before getting the canadian paperwork is not an option.)
And one more question:
3. Has anyone ever been denied residency based on CSQ by the federal? (No illness, crimes etc.. Trilingual Candidate with degrees from europe and the US)
Thanks for your help. Please be as clearly as possible with your answers.