I just got an iPhone 5, downloading apps is free with Wi-Fi, right?

I just got the iPhone 5 with AT&T, and I know data is free while on Wi-Fi, but is downloading apps also free because I'm on my Wi-Fi? What I'm concerned about is the second I leave the house and have no Wi-Fi, all the apps I downloaded will then go against my 1 GB of data. Will it do that? Or is it just a one time thing as long as I download it with Wi-Fi?

Also, What does this mean: "Turn off cellular data to restrict all data to Wi-Fi, including email, web browsing, and push notifications"

I'm assuming that I should click that to "off" and not "on" It's off right now.

Added (1). Okay. So let's say I'm at a friends house who has no Wi-Fi, and I want to play one of the games that I downloaded that doesn't require Wi-Fi, will it use data to play the app? Or no?

Everything with Wi-Fi including apps won't charge your data. But once you leave the Wi-Fi area everything will be against your data. Every notification you get even emails. But if you're on Wi-Fi it won't waste your Wi-Fi.

When you download an app it is free with Wi-Fi as long as you stay at the place with Wi-Fi but make sure the apps you get are free too or you have to pay for the app and when you turn off cellular it doesn't let you go on the internet without Wi-Fi so even if you accidently open up safari it won't work without Wi-Fi but if you do turn it off you can turn it back on at anytime.

If you are downloading free apps from the app store while on Wi-Fi it won't cost you anything! Wi-Fi is free and it will tell you if the app is. They will work when you leave the house as long as they are not games or certain apps that require internet access-Wi-Fi or Data.(Facebook, twitter, etc)

Turning off your cellular data means that when you don't have Wi-Fi and you want to use your data you must turn it on to allow access onto your social networks, safari and certain apps. When its off and you don't have Wi-Fi your notifications and emails will not come in. I keep mine off at home and if I usually have it on when I'm out. 3G, 4G, or LTE is what you enable to use your data and surf the web faster.

Hope this helps!
Enjoy your new phone!