GoogleFit REST API vs Native(Android) API?

Question

Google

1. How accurate are these approaches?
   
2. Will the Android API work on iOS?
   
3. In theory , REST relies more on GPS, while the Android API relies on raw sensor data and the same ones filtered from their server, right?
   
4. After all, how else can they determine by API how much the user has passed, calories, height, weight, especially the heart rate, and so on?
   

Google Fit APIs
Android and REST APIs to access the fitness store. You can create apps that support Google Fit on multiple platforms and devices, such as Android, iOS, and Web apps.