Best way to store high scores locally and on Facebook SDK

Hi all! I'm looking to add a social scoring system in my app for Android and iOS, basically a leaderboard. I'm planning on using Facebook (correct me if it's not suitable) SDK for this purpose. As I am fairly new to server side stuff, I have a few questions!

1. How do I go about storing user's highscores? Should I save them under PlayerPrefs and then everytime when the app starts, check if playerprefs highscore and the one on Facebook is the same, and if it is higher update the one on Facebook?

2. Since my app is going to include in-app purchases, are the user's purchases going to be stored based on his/her facebook account? If so, restoring purchases should be linked to the user's facebook account?

3. Or should I just stick to native leaderboards such as GameCenter or GooglePlay?

Thank you!