There was just a talk on this at my school.
I'm not sure the difference between T1 and T2 relaxation times (must not have been paying that great of attention, ha), but the reason you can use gadolinium to image tumor cells is that the tumor cells don't have a blood-brain barrier. They just want a ton of blood so they can keep growing, so they aren't selective. Therefore, the tumor takes up the gallium and it shows up in the MRI, where the rest of the non-cancerous brain just looks grey because it hasn't taken up any gadolinium.