"WhatsApp" works using the internet.
You can send messages and chat with anyone else, for free - as long as they have the app on their phone as well.
When I say, "for free" - it's free, as long as you don't go over your internet allowance, so if you pay for your internet on PAYG, you'd need to check how much it would cost, but if you get a monthly allowance, then as long as you don't go over your allowance, there are no more costs involved.
If the wifi in US is free then Yes. Important to reiterate you can only call people who are also have WhatsApp on their device, you can't just ring any number such as house phone.
As far as I'm aware, that is correct.
Your only cost, is the internet usage, so if you can connect using someone's Wi-Fi for free, then there will be no costs involved :)
If you look at your contacts in WhatsApp, it lists all the contacts that are on WhatsApp first. After that, all your other contacts have an "invite" button highlighted next to it, so you can invite them to download the app.