There are many ways to make your rank up. But surely, this doesn't take a short time. There are some ways to earn points, it is: answering questions, voting for best answer, verifying email address, logging in, setting avatar, giving the best tip, having a tip liked, having a question liked, and so on

Sure, you can. You must be connected to the internet first. You can play multiplayer against people in the world (providing they're in the same room at the current time). There, you can host your restaurants or play with anyone else's restaurant (which you may possibly not have yet, or their own My Diner). You can host new restauants by making your own My Diner or purchase additional restaurant, or unlocking the other  4 restaurants (ballpark museum, boardwalk, disco)