Is it possible for my mobile carrier to track my wifi usage and bill me accordingly? I watch a lot of inspiration videos from TED (www.ted.com.au) on my new Galaxy S2 phone. However, I only do this when I am at home and can access my home wifi network.

My home wifi and the phone's 3G networks are with different providers. Obviously, my phone switches to the home wifi network automatically when I am at home.

My question: Is it possible for my 3G network provider to see/track my wifi usage and bill me accordingly (as if I am using the 3G network) because everything goes through the phone that is on their network?

I am new to smart phones so please bear with me. My monthly 3G data download allowance is only 150 MB but my home wifi came with 5 GB.
Of course not. Your WiFi will go through your WiFi chip to AP and to some other ISP. There is no connection with 3G just like you can use WiFi even without SIM.

But your carrier can(though highly unlikely) use some tracking program to track you and find what you are doing. Even if they do, the WiFi usage won't be counted as 3G.

One advice I'd like to give you is sometimes you think you're on WiFi but due to many reasons you might not be connected to WiFi and you might be browsing over 3G. So just keep an eye for that.