I've installed Oracle Cloud app with hope that I can manage my instances(turn them off, on or restart) but I can't see such option. Is there a way to do that within app or It's just a health status?
At present you can not turn things off and on again via the app. Currently (30 Nov 2020), you can view details about the following types of resources in the mobile app.
Compute instances Block volumes Object Storage Load balancers Autonomous Transaction Processing Autonomous Data Warehouse
You can find its current documentation via here - https://docs.cloud.oracle.com/en-us/iaas/Content/GSG/Concepts/mobile.htm