Correct. Don't overthink this too much, especially before you even get your application sent in, otherwise, you'll stress yourself to death. Just take a deep breath and take it one step at a time. If at any point they have a question about his medical or claim they can't find it, you can send them a copy of your receipt so they can hassle the doctor .. I mean, so you can prove that he's had the medical done
Yes, keep either the original (if not required for your application) or photocopies of EVERYTHING you send in to CIC, including your actual application, so you always have reference to and availability to get to paperwork if it needs to be given again for any reason.
It is a long journey, but it doesn't need to be totally stressed out. You've already found, IMHO, the single best source of information regarding immigration to Canada available to you.