The first thing is that after your application is approved, you will be issued a PR visa (single entry) along with the COPR. You have to enter Canada before the expiry of the PR visa. In most cases the PR visa is valid for 6 months, expiry of the medicals (1 year), expiry of passport of any of the family member in the application; which ever expires before.
If you child is born after your receive the PR visa & COPR, but before you land, you can add your child to the application, and IRCC will cancel the existing PR and COPR and issue you a new one for all members, including your new born.
You can only add your child after it is born. All you need to do is send your newborn's passport, medicals, birth certificate and forms. You will also have to make sure that your PoF now meets the family size which includes your new born.
Also, the secondary applicant cannot land in Canada before the primary applicant. The primary applicant has to land before, or along with the secondary applicants.
1. Re-medicals are only requested if your medicals have expired. If they are valid, then no remeds are requested and if your medicals are about to expire, IRCC may even extend them.
2. You can only add your newborn after it is born. As soon as the baby is born, gather the above documents and inform IRCC.
3. You can renew the PP any time, before or after, it does not matter. If you renew before, send the scan of the new passport to IRCC. Ideally you should renew it before, so that your PR visa can be issued in your new passport, just for convenience, although it does not matter.
Also, be advised that after the PR visa is issued, getting extensions is very difficult. So plan accordingly.