How to skip the first facebook credential prompt?

I’m writing a hybrid app with Ionic and the workflow I imagine for a perfect facebook integration would be the following:

Scenario of a user logged in facebook with a native app:
1 - Open my app
2 - Touch login with facebook
3 - Be prompted for facebook permissions and approve
4 - Be directed to the desired screen of my hybrid app

Scenario of a user logged in facebook with his mobile browser:
1 - Open my app
2 - Touch login with facebook
3 - Be prompted for facebook permissions and approve
4 - Be directed to the desired screen of my hybrid app

Scenario of a user not logged in facebook (both in the native app and mobile browser):
1 - Open my app
2 - Touch login with facebook
3 - Be prompted for facebook credentials
4 - Be prompted for facebook permissions and approve
5 - Be directed to the desired screen of my hybrid app

Is it possible to achieve as the mechanisms used to save session of a native app and a web app (facebook website) are way different?

How can I know if the native app is installed and once I know how can I use its session to prompt the user for permissions (as the android native apps do)?

Thanks in advance