DRESS - Start leaving some clothes at work on days you drive, and wear bike clothes on your commute. I can't imagine commuting 16 miles each way in street clothes. That must be very uncomfortable and sweaty. I leave shoes, pants, t-shirts, towel, etc. in my office. I carry clean shirts, underwear each day in a large seat bag (Carradice Barley).

BIKE - No harm in riding your mountain bike, but I would add a rack so you can put panniers in the rear, or use a large seatbag like a Carradice for carrying gear. Definitely put slick tires on your wheels; that could improve your average speed 1 mph or better, particularly if they are light folding tires. I would hold off on buying a new bike until you are sure that you will keep it up, but eventually plan on getting a cross, touring or sport touring bike made for carrying gear. I commuted for 2+ years on an old steel Italian racing bike using my Carradice bag, but bought a touring frame last winter. The touring bike is a little slower but much better for carrying gear.

LIGHTS - Check out the Magicshine LED light. There's a long thread in the Electronics & Lights forum here. Dinotte, L&M Stella and Fenix L2D are other relatively inexpensive front light options (altho not as cheap as Magicshine). For a tail-light, check out the Planet Bike Superflash or Dinotte 140 if you want some real firepower and don't mind spending $100 on a tail-light.

TIME - Your speed is not bad for a mountain bike with knobbies. Adding slicks should improve your time a lot. I average 15 mph year-round riding a road bike on hilly terrain with about a dozen red lights on my route.