There is no way to solve Casper's problem. You can either kill the white chicken (in Bellegar's shrine nearby) to put him out of his misery, or do nothing. My first time through the game I tried herding the chicken towards Casper (since there was no way to tell him where it was), which became a tad frustrating. I killed it out of annoyance, which was rather funny; not the actual killing, but
You can not do anything for Dr Needleman, either. Without his helmet you cam mindread him to get the password to his storage area (not that there is anything of value there).