You definitely don't want to apply before you have 3 years physical presence as this will automatically require an interview with a citizenship judge where you must explain what is so special about you that you should not be subject to the same rules as everybody else. You will also have to wait much longer than otherwise and you might not even be approved. It is much better to wait.
You should have some piece of paper, either a COPR or a Record of landing but not both. If you have lost it, you can apply for a copy, see
http://www.cic.gc.ca/english/information/applications/certcopy.aspThere is nothing you can do to speed up your citizenship application.