I did not specify, but WhatsApp also uses mobile data connections such as 3G/H+/4G to send/recieve messages and calls.
To tell if they've seen your message, when you click send 1 grey tick beneath it will mean it is sending to your contact. 2 grey ticks means it has delivered to the person, and when the 2 ticks turn blue it means they have opened WhatsApp and read your message. If you're calling their phone should buzz like if you're calling them normally (as long as they have an internet connection). Hope this helps