3G CAN be to do with internet but it does voice as well, the data side is faster than 2G.
Your handset will grab the best signal it can, ie if its set to both it will go between them getting the strongest signal it can and using it. If you set to 2G only you will only use the 2G network, save battery and if you dont use the net on your phone its a good option.
Yes I would imagine O2 do use it, but maybe not in your area. There needs to be specific equipment for 3G on the masts, if you live in the sticks they probably cant be arsed to fit it as its costs money and they will never recoup it. Or it could be switched off for reasons unknown.
Not sure if 4G has been released where you are or in the UK, was rolled out in Malaysia when I was there a few months ago. either way, use 2G only if you dont use data much.