Is it possible to make my game with a friend through internet, to edit it together at the same time?

I think that if neither of you plan on using the offline editor and downloading the game file from a private posted page, I think the only way that could be accomplished is if you shared the password to your profile so you both have access to the Create page once you are logged in.

I'm not 100% on this, so if I'm wrong someone please come along and correct me.

You'd be better off doing it in the desktop version, and putting your game file into a shared dropbox folder or similar. There's no way to reliably share real time updates so you'd have to co-ordinate it so you weren't editing the file at the same time, otherwise you might inadvertently overwrite each other's updates.