Welcome to Android Central! Which carrier are you using? When you talk about using wi-fi for calls and texts, do you mean using something like Hangouts Dialer or Skype? Or are you talking about wi-fi calling, like through T-Mobile? If you turn off data (i.e. 3G/4G), calls you make would still be over your voice signal (including if you have wi-fi calling turned on, like on T-Mobile). In order to use wi-fi exclusively, you'd have to turn on Airplane Mode, then turn wi-fi back on, and use something like Hangouts Dialer. In that situation, your calls wouldn't show up on your phone bill. But you can't send SMS if your voice signal is turned off (although you can send other kinds of IMs over wi-fi, like Hangout messages).
We need to know which carrier you're using before we can try answering the question about available wi-fi connections. If you have Google's Project Fi, I believe it has to be an open public wi-fi network, through which Fi connects after setting up a VPN.
If you have both wi-fi and mobile data turned on, the device will switch back to mobile data if it loses the wi-fi signal. You'll know that mobile data took over because the wi-fi icon will disappear from the status bar.