Yes they can repaired very nicely, I did one many years ago at a a Corian class I took. I still like corian.
What is the damage from heat on granite? Spalling, cracks, discoloration? I have not seen any
If you continually use an area on granite as the trivet, it can potentially cause a stress crack over time from the expansion and contraction... technically, you can use a knife on granite but would end up dulling your knives, and again, potentially find light scratches in the finish...
It all comes to using the countertop the way it was intended to be used... it's not supposed to have hot things set directly on it, cut on it, mix stuff with red dye in it, etc... these surfaces are heat-resistant, scratch-resistant, chemical-resistant, etc. not proof... going outside these parameters and doing those things is considered abuse and generally not covered under warranty...
Why would you spend that kind of money to use it in a way not intended anyway?
When it comes to Corian, these are surface stains and on sinks a maroon or green scotch-brite pad and some Soft-scrub will remove most any stain in the sink... don't use the green one on the countertop as it might dull the surface of a gloss or semi-gloss finish...