You won't be able to send the phone to 3 for repair because it wasn't obtained through them. Samsung won't help because there is technically nothing wrong with the phone. You've also voided the warranty by rooting the phone anyway.
As far as I know, 3 don't use specific firmware that will only work on their network. If your problem is data and you can make and receive calls then simply go to Settings > Wireless & Networks > Mobile Networks > Access Point Names and create a new APN with these values...
MMS proxy: mms.three.co.uk
MMS port: 8799
Authetication type: None
If the fields above are blank they don't need anything in them and should say <Not Set>
Then set it as the default APN and delete the other in there. Does this help?