By store data, I do not mean saving it I just mean temporarily storing it for later use. I've been wondering this for a long time, and is it possible to do this? (I mean storing it without it being an object such as a value that has a parent and stuff)
I'm a little confused as to the purpose of what you want to do, but you can put a modulescript there and then store info in the instance of that modulescript that is created the first time you call the modulescript using 'require'.
From the wiki however: "If you would prefer a secure storage place, which the client cannot see or interact with, see ServerStorage." Also keep in mind replicated first is local. I never actually tried storing anything in it.
Of course as you say, a new server will not have access to the data stored there in a previous server.
I don't know what you mean but yes it is possible, if the game is filtering enabled then you should use remote events in order to access the storage you are using.