Saving: using the webstorage plugin (examples of use listed in the section "WebStorage" of the how do I FAQ) is one way to go.
Another is to use AJAX to send the datas to a server, and store the datas there. Check the how do I FAQ to the section AJAX.
You can also check at this example of level editor (basic, WIP) with saving.
Multiplayer is possible, but requires you to know how to code the server yourself.
Check the how do I FAQ to the section "Multiplayer" for the starting tracks.
You can also check the third-party plugins some like "Chat", "websocket" are what you are looking for.