is that a Y Combinator?

You bet!

(Actually, it's a 'fancy' Y-combinator that also allows for mutual recursion, but I think Scheme optimises it down to a regular Y-comb if it sees you're just doing single recursion.)

I've been trying for two hours to figure out how to answer this question, and I still don't know how. But I managed to write sum in terms of the Y-combinator:

; Namelessly add 2 + 2
(((lambda (X)
    ((lambda (proc)
       (X (lambda (arg) ((proc proc) arg))))
     (lambda (proc)
       (X (lambda (arg) ((proc proc) arg)))))) (lambda (func)
                                                 (lambda (ls)
                                                   (if (null? ls)
                                                       0 
                                                       (+ (car ls) (func (cdr ls))))))) '(2 2))

Hoo-ah. I, uh, don't think I'm going to attempt to unsugar the code that's using the letrec. (I can't show it to you yet. It's a secret.)

Does he not like to be called Dr. Stone?

I got into the habit of calling the CS professors "Mr." and "Ms." because they've been listed as such on the departmental website for as long as I can remember.