question

>What should I do if that player buys a new device and the facebook (or other option) is already linked?

Actually, you don’t have to concern about this issue. Since the Facebook account is linked, you can always login into your account via LoginWithFacebook, and no matter what device you are using, as long as you keep the Facebook identity, you can always access to the same account you have previously linked. Once the player account is linked with 3^rd party platform identity or custom ID, unless you unlink it via API call or Game manager, PlayFab will always keep those identities and changing the device will have no effects on it.

> Since the player is on another device, how do I find if it has the facebook link to provide a login button instead of a link button ?

You can use GetAccountInfo to retrieve player account information.

> Should I have a Create Account/Login Existing Account UI since the beginning?

It is always necessary to have both create new account UI and login into existing account UI in your game.