How can I remove microabrasions and dark spots from airpods' case?

You could give Bon Ami Cleaner a try to get the dark spot out.

As for all of the scratches, I guess you'll need to get one of the skin makers to make one up for you ;-}

Think of it this way: Mountains & Valleys. To remove the valleys we can push the mountains into them smoothing out the land.

Sadly, we don't have any mountains here ;-} All you can do is remove the surface area to match the valley of the scratch (bringing the surface down to the same level). A polish basically does that just at a microscopic level so small scratches can be hidden. Bigger scratches may require a more aggressive polish or even sandpaper.

But there is a down side here! As the more you polish or even sand the more you are removing the finish which can expose the base material which may not be pretty!

Give the Bon Ami cleaner a try it is a mild polish and cleaner. Beyond that I think you'll need to get a cinch bag to hold the Air Pod case or put something over the case to protect it.