I had lost hope with my electric cooking plates. The white circles where completely hidden under a layer of diamond-grade burn residue that no amount of scrubbing with chemicals could even begin to remove. I found this 3€ scrapping tool and it’s amazing !!! Sorry, but I don’t have the before picture, believe me after 6 years of usage, it was bad.
Depends on the hardness of the metal you would need a metal.
These stoves are mostly aluminium oxide, which has a mohs hardness of 9 and steel is 4-8.I looked more into it and I found glass ceramic stoves have a mohs hardness of 6-7. So a very hard steel should be able to scratch it, but most steels including stainless should be fine.