Oh boy, that isn't something a pro could pull from the fire. My reccomendation is (A) spray all dark places with bleach water then wipe after a few minutes (B) after surface is completely dry, apply tape just above discoloration and on accross back (C) apply 2 coats of Kilz, Binser or similar (D) paint a color close to cabinet color. Do the same for the spot under drain line , make a square with tape.

You cannot stain the water damage. It appears to be pressboard to me (so a paper cover).

You can paint, you can buy wood-look contact paper, you can place a panel over it, you can cut out and leave the wall exposed, you can replace the back.