How do I deal with user metrics?

Is it possible to have and study user metrics, such as: where a user downloaded the app, if they used the app,if they came back to the app, if they referred the app and, there spending habits on the app - in other words their acquisition, activation, retention, referral and Ltv?

Much of this is handled on Google Play, the rest, you would need to code blocks to capture the information and return it to an online resource - you should advise users that user metrics are being monitored and ensure you protect their privacy and personal information in doing so.