If I have a character in my resource row (face down) and it gets replaced (or KOed), do I gain endurance when the character goes into the KO pile?

no. only characters that are "in play" will gain you endurance.
"in play' means characters in your front or support rows. or characters that were recruted or put in play by some effect.

hope this helps.

There is an important distinction between characters and character cards. When a character card is in the front row or support row, then it is also a character; character cards in your resource row are not characters, and so cannot trigger Gone But Not Forgotten.