Cooktop is scorched/burnt. Not removing them completely but you may be able to lessen them with Weissman Cook Top Cleaner.

No fixing that cost effectively.

If you can't feel anything, then it's probably not removable, but glass that's been scorched, as millworkman says. I had that happen on my first glass top stove from using an aluminum steam canner on it. I think it was partially the high heat and the aluminum combo. When I got a new stove I also bought a hotplate to use with the canner and I've had no more problems. You really need to keep the stovetop free of spills and use special cleaners so they don't scorch. I clean mine practically after every use, because something always seems to spill or dribble.

Look at youtube about how to scrape off burned on food with a razor blade. If anything will come off, that will do it, but you have to use it properly or you'll scratch the glass. I use ceramabrite or Sears glass top cleaner. You can also try soaking it with distilled white vinegar (let it set a long time, then sprinkle with baking soda to see if you can scrub any of it it off) to remove any minerals from water that may have hardened on it.

If you can't get it off, you might see about replacing the glass top instead of being charged for a new stove. I cracked a glass top once and replacing the glass was $$$ but about 1/2 the price of replacing the whole stove.

https://www.youtube.com/watch?v=MnvBrMehn_k