The TPMS is two parts, the valve, and the sensor. You can replace the valve stem when needed and reinstall it on the old sensor.
The TPMS goes to sleep when you stop. While you're driving, it broadcasts once per revolution (I think). So, it sort of depends on how much you drive. Most will last at least 5-years or so. After that, it's hard to say. There are test tools that can activate the sensors and report the battery status, its ID, and the tire pressure. Since the test tool gets the battery status, I'm assuming the vehicle does as well. From what I've seen, when that happens, the car displays TPMS failure. Internally, it knows which one(s) are bad, but it doesn't display that. On the two BMWs I own, my older one says failure, and then won't show the status for any of them (which I think is dumb!), so you don't know which one it is. That info is probably available with a BMW OBD-II reader, though, or their diagnostic computer.
Each TPMS has an embedded ID code, sort of like an ethernet adapter, so once the car learns which one is where on the car, it can report data fairly quickly once you start moving. During a reset, it listens for each report and since it doesn't know where they are, and they could be trying to talk at the same time, it can take awhile. Then, it has to figure out where they're located. I think it does that by trying to figure out which tire is rotating at different rates as you go around curves, otherwise, they'd all be going the same rate, and the reports would all occur at the same intervals. The i3 does not have multiple TPMS receivers...there's' one, so it has to do some calculating to figure out which one is which and where they are located.
2011 535i x-drive GT, 2014 i3 BEV