You will know if the TPMS are working because if they are you won't see a light blinking at you on the dash every time you start up the car. They are installed inside the stem. I got the Blizzaks w/ wheels from tirerack w/out the sensors so I see this light all the time.
Unless you are really trying to save tread life on your tires I wouldn't go through the hassle of having to mount and dismount your winter set up each time you need them. Just make sure you don't run them too long after winter because they will wear tread very quickly in warm weather.
Good question about the PSI, I pumped mine up to about 39 PSI, which I think is probably a little high, but I was worried about mileage. The Blizzaks have a PSI range of 34-44 I think, so I decided to split the difference. Anyone know a good PSI to run?