A fine balance
A: No. Don't begin your career by taking sides. Separate the professional and the personal. Your head of department is entitled to expect that you will manage your working relationship with him or her on a purely professional level, without all the baggage of second-hand interpretations of someone else's problems. Your friend should relate to you as a colleague and not seek to enlist you in petty feuding. Do your job as well as you can and you'll earn respect from all factions.