Is there anywhere online where we can buy a set of small sand paper pieces? Or do we have to go to Home Depot and curate our own collection of various grits?Different grits of automotive sandpaper. You best start with the same grit as what caused it. From there on you follow a progression up to the finest one. Say P120, 240, 320, 400, 800...
Stainless cladding is usually both very soft and abrasion resistant. Damage occurs easily and gets just as easily repaired — as long as you can live with some imperfections. Please remember it's a tool you're handling and more blemishes will appear over time. I admit that this one is nasty on a pristine blade. What I mean is you shouldn't expect a perfect result. An acceptable one is good.
The hardest part is in avoiding to cause extra damage with the first grit, especially on the matte side and the tip. I would use a loupe (around 10x) to check the tip. Once done, your tip will need a sharpening touching up.
You should either refinish the entire wide bevel on stones, or relax and forget about it. You’ll never be able to fix just the core and make it look good. At least, I wouldn’t be able to.Due to a series of unfortunate events, the knife is scratched even more. How do I get rid of this line scratch on the core? Very carefully rubbing with a tiny nagura?
Leave it and sharpen, starting far behind the edge — as you always should. The patina will disappear, but reappear as soon as you are going to use the knife again.Leave it. The reason it shows so bad is because of the contrast of the patina. Any fix will remove more patina. Using the knife will bring back some of the patina.