How can I tell that my phone uses the Wi-Fi connection for data traffic?
If you are connected via Wi-Fi, your phone will only use that connection. The only sort of data that would be required to use mobile data would be MMS (aka multimedia messages) everything else will operate with Wi-Fi if you have it.

One thing you'll also want to look into is the Wi-Fi sleep policy, to ensure you phone never disconnects from Wi-Fi if it is in range.

Go to:  

Settings → Wifi → Advanced (via menu button) → Sleep Policy


Set this to "never", so your phone will always use Wi-Fi (if available) when it's asleep.
 This also saves battery as the distance between your Wi-Fi and your phone is a lot shorter than the phone mast and your phone!

Update
If you are that concerned about using mobile data, search the market for "APN Droid", which is an app that completely turns on/off your mobile data.