Data used on a Wi-Fi connection does NOT count against the data used in the phone connection to the internet. Remember: There are 2 separate systems. One is Wi-Fi and the other is the data plan from your phone company. The Wi-Fi side will NOT work if you are one of the Pokemon Go searchers wandering around searching. That game is a super data hog and very few of the “target” sites have free Wi-Fi. My house is one of the “targets” here in Vegas. (without my consent incidentally, but that is an issue I am taking up with the game owners!) My home Wi-Fi network is visible to all devices within range, but has very good password protection. I have also had to post my property with No Trespassing signs because of the morons who decide that they can go anywhere they want while playing the stupid game.
The data plan is only when using the phone through the non-Wi-Fi, built in internet feature that is part of your telephone company’s plan. (Out of range of a Wi-Fi source) A Wi-Fi connection is a completely different thing than the phone company data system.
Want free Wi-Fi? No problem. Connect via someone’s internet connection through their Wi-Fi router. (Assuming they give permission and give you the password to join. A worst case scenario is to find a location (many fast food places, public buildings, etc.) that offers free Wi-Fi internet connection. Just be advised that a place like Starbucks will expect you to buy something periodically if you are sitting at one of their tables and using their free internet.
Around my house, all of our wireless devices connect to the house Wi-Fi router network shared with the computers. The only time data from the paid “plan” is used is when out of reach of the router.
BTW: You do NOT need a telephone connection to connect to a Wi-Fi router on most smart phones. That is a separate phone internal system. (The phone becomes a small and low powered computer only and is useless if away from the Wi-Fi router’s range.)