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 t$$anonymous$$s purpose. As I am fairly new to server side stuff, I have a few questions!

1. How do I go about storing user's $$anonymous$$ghscores? Should I save them under PlayerPrefs and then everytime when the app starts, check if playerprefs $$anonymous$$ghscore and the one on Facebook is the same, and if it is $$anonymous$$gher 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 $$anonymous$$s/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!