Is diet coke bad for a diabetic?

No. Sugary liquids are not good choices for diabetics. Therefore, diet drinks are acceptable in diabetics.
Depends. Depends if the diabetic likes caffeine, phosphoric acid and all the artificial sweeteners. The caffeine could upset the stomach and worsen reflux in a adult onset overweight diabetic. You would be better off with water infused with fresh ginger, or a leaf of mint. Healthier than the processed stuff.