To download Swisscom's blue TV application to the Mi TV Stick with Android and HDR support, you can do so directly from the Google Play Store, as the device runs on Android. However, I'm not sure if the blue TV app is compatible with all Android TV devices, but generally it's available on many Android TV devices. To watch live channels, replay and recordings, you would need to check the specific compatibility with the blue TV app and Swisscom's terms of use.