When I am away from home and using Verizon wi-fi on my iphone, am I being charged for data?
Data usage on your wireless account is cellular data, not WiFi data. WiFi data goes to the internet connection providing the WiFi access.
No, your iPhone would only use your Verizon wireless data plan on the 3G & 4GLTE networks, if you're connected to a Wifi hotspot instead you'd be using that for data instead
You need to explain what you mean by "Verizon wi-fi". If you have a hotspot on your account and you connect the phone to that you;re still using your Verizon data. So that's kind of pointless.