Kitchenaid stove problem

i have 2 problems with current Kitchenaid Superba ceramic top stove-
1: dual element does not work properly - the smaller element does not light up by itself, it always lights up together with the larger, outer element (does not matter on position of the knob) 2: ceramic top seems to be "microscopically" scratched. The previous owner did not use the "recommended" cleaners, but regular household stuff - Vim or something. The top seems to be attracting spills better, often burning them onto it, making them very hard to remove. That makes me think the top might be scratched somewhat (no visible scratches though).
Is there something I can do to troubleshoot the problem 1? Is the ceramic top cleaner required for cleaning, and do other cleaners damage the top, or is it just in my head? if there is a chance the top is scratched, is there a product to restore it to original condition ?
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