The support site can be a great resource for any questions you may have about the app and your controller. As for your specific questions, I can answer those for you!
1) Here is a link describing how to install the WR2 on your controller. Once it is properly installed, make sure to enable it in the app by going to "Device Settings" and turning the rain sensor on. When the sensor activates, you will get an event in your "Device Updates" section of the activity feed, and all scheduled waterings will be skipped until the sensor deactivates. You will still be able to manually run if you would like. If you would like to test your rain sensor, there are good instructions on how to do that here!
2) I have also noticed that the app selects a station when you view more details. This is a design flaw, and we hope to improve this experience with our upcoming software update! I apologize for the inconvenience it may cause. As for the NOAA stations not showing correctly, I cannot say I have encountered that. Did you toggle PWS on and off again to see if they appeared then? As for selecting a backup station, we do not currently have that feature. However, if your selected weather station begins to fail, we do default to the nearest national weather station for data, so you should be good selecting the PWS that is closer to your home, as long as the data looks accurate to you!
3) You should be able to use the same credentials for each platform (iOS, Android, Web.) Are you sure you are entering the correct username and password? If you would like me to look up your username or send you a password reset email, please let me know.
4) We estimate your usage by using your zone size (in advanced settings) and your nozzle precipitation rate. If those are accurately set, your usage should be fairly accurate! If you need help determining nozzle type, there is a good article here describing the types, or I could help you determine those!
Let me know if that all makes sense, and if I can help with anything else!