I am now in a certain phD program, but if I am allowed to answer:
Regarding the first question, the answer to my email question varied from one program to another. I think you should consult the department or the university directly. (That being said, I guess, in most cases, it will not matter which department code you enter, as long as you send the scores to the right school)
Regarding the second question, I have no definite idea.