G3 or 3G? Either way I don't know much about it and how secure it is.
Personally I'd probably not do online banking over a mobile phone network, purely because I don't understand the security implications and 'hackability' of such a network.
As for using your credit card and online banking on your work's network, some would say it's overcautious and some would say not. At the end of the day you should do what you feel is comfortable. If the IT bods really really wanted to, they could probably do it, but (a) they'd have to be monitoring at exactly the time you do the transaction and (b) they'd have to want to do so.
Doesn't help much, does it?