yes, the approval paper, known as COPR (confirmation of permanent residency) does have an expiration date. No one can really tell you how long the COPR will be good for in your case because there are many factors it depends on, and the expiration date is set by CIC. Yes, it is generally on or a few weeks after the anniversary date of the medical exam. CIC has the ability to extend the medical exam if necessary. Currently, US applications that are straightforward and not complicated are being processed in 3 months. First rule of this forum - do NOT go by the posting processing time online for visa offices. They are not updated, and do NOT reflect TODAY'S processing time. Of course there is no knowing how long this "trend" will last.
Technically, since you have been married over 2 years and have a child, your wife won't have the "condition 51", which means she must cohabitate with you for 2 years after approval. So this means, she can technically "land" as a pr, then go back to the US to finish her studies. Note that any time she spends living apart from you will not be counted toward her permanent residency requirements. To avoid this, she can "land" as a pr in canada, then you guys can go back to the us together until you are ready to settle in canada. As long as you are living together, it counts toward PR, no matter where in the world you are. The only hiccup here is that in order to be approved, you must prove your intentions to move back to canada upon approval, so if you suggest staying in the US after approval, it may not result in a positive determination of the application. If you guys are not ready to move back yet, then it may be best to wait until it gets closer to when you plan to acutally move to canada.
Yes, you will need to prove to CIC that you intend to move back to Canada upon approval. this is a very standard piece for those living outside of canada at the time of the application. What people do is write letters and show a plan of where they intend to go, research done on areas, real estate, communities, job search possibilities, etc. Also, if you have family in canada, it's usually recommended to have family write letters showing their support and agreeing to help you get settled, by offering a place to stay, etc. Basically CIC wants to know you will not apply for welfare the minute you get there. The plan doesn't need to be concrete, it just needs to make sense.
Again, if you don't think you'll be going to canada anytime soon, it may be best to hold off on the application until it gets closer to when you will actually move to canada. Before OTtawa started fast tracking applications, the average seen on this forum was 8-10 months for processing, so ti's a good idea to start with that time frame and go from there. Again, don't go by the 15 month processing time. it isn't a "true" average, and i believe it is reflective of agency wide strikes and office closures. of course, the approval time may change again, it's just impossible to predict.
Good luck!