A:AnswerIf your Moto Z is an Android, then yes. To answer the second part of your question, the answer is also yes. I cast Netflix or HBO GO while utilizing other apps on my phone.
A:AnswerI've gotten this to work with various sporting event websites. If you are streaming from Chrome I think it will cast anything. If you are using an app, there may be restrictions. But with an Android tablet you can just cast your screen and anything on it.
A:AnswerBe sure you are connected to the same WiFi network as your Chromecast device. Then, in the Google Home app, look for the option to mirror your device's screen to your Chromecast.