Is Android Studio must for Flutter?

It is not neccessary, but advised to install Android Studio for Flutter . It makes it very easy to install and configure all the settings etc. What you definitely need is the Android SDK and JDK. You can definitely install and run flutter without Android Studio (you can also use Visual Studio).

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How do I integrate with Firebase?

Open the Firebase Assistant: Tools > Firebase. In the Assistant pane, choose a Firebase product to add to your app. Expand its section, then click the tutorial link (for example, Analytics > Log an Analytics event). Click Connect to Firebase to connect your Android project with Firebase.

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