I am not sure if I am interpreting the question correctly per se. I drew a picture in which Clark was diagonal from Diana. So, that means Chris could either face Clark OR Diana.
If Chris is facing Clark, then Chris tees off first and Diana tees off second. If Chris is facing Diana, then Doug tees off first and Diana tees off second.
Either way, Diana tees off second.
Did I interpret the question right? The part about "Chris is facing the person whose name begins with the same letter as that of the name of the person who will tee off first" sort of tripped me up a bit. I used this piece of info to determine that Diana tees off second and it is impossible to know who tees off first.