Even if you have researched your things, I still want to place this "
So You Want To: Write A Minor MMO" link here.
Also if you can't figure out the most basic networking/serialization part, you're in for a very rough journey.
Besides the question not being related to SFML and you probably getting more/better help at dedicated gamedev communities, I'll still add some basic layout that you probably want to follow for a multiplayer game:
To prevent client side manipulation/hacking, all the physics and action should happen on the server side. All the client essentially sends to the server is the user input. Then the server validates these inputs and simulates the new position/action/etc. and sends that information back to the client. In the meantime the client simulates the physics as well and for example moves your character forward, but if the position from the server doesn't match the position of the client, the client will reset to the information of the server. That way you can't just move your character to position X and the server will accept it as a valid movement/position.
This is the simple client/server setup. From there you'll have to expand to multiple clients, meaning that all the position and effects of the players, NPCs, etc. need to be send to every client and every client's input has to be taken into account in the physics simulation.
That's the basic layout of a "modern" MMO and thus I really suggest to you, to start with some basic single player games first, then maybe move to a multiplayer and only after a lot of experience pick something like minor MMO.