question

First, if players will be hosting their own game servers, it's important to note that those servers must not have any ability to call into the Server API set. To do so requires the Secret Key - which you do not ever want to have in the hands of anyone outside your team, as it allows them to make any calls they want to in the Server and Admin API sets. In other words, they could basically delete everything about your game.

So the client-hosted version of your server would use Client API calls, and make calls into Cloud Script occasionally for server authority when needed - like evaluating the points reported at the end of a level, for example.

As to cross-platform play, that part is simple. The client and server exchange data packets that contain the information they need from each other. Nothing about that data is platform-specific, so yes, you can have players from different types of client machines playing together. The exception to that would be where there are specific policies from platform owners preventing this. For example, you cannot enable cross-play between Playstation and Xbox consoles - that's specifically prohibited by Sony and Microsoft policy (though Microsoft has said they would allow cross-play if it's via Xbox Live, of course).

So one important thing to do is to review the policy documentation for any platforms you intend to ship on, to make sure they allow the things you have in mind.

Now, once you're past that, you'll want to have a look at this guide, which describes how to enable externally hosted servers in PlayFab: https://api.playfab.com/docs/external-server-hosting. That's specifically the information you'll need to have a client-hosted server register itself in PlayFab for matchmaking.