Would laser resurfacing help with facial hair and or small veins on the face?

Resurfacing lasers are typically used to treat fine lines and wrinkles, textural abnormalities, and scarring.  Removal of facial hair is typically performed with different types of laser, ones that targets cells in the hair follicle.  Likewise, small veins on the face are removed by lasers that target red blood cells inside the vessels to ablate them.  So, while lasers can certainly be used to accomplish both of the things you mentioned, it is not specifically a resurfacing laser that will accomplish the removal of hair or vessels.  Best wishes.

Laser resurfacing removes fine lines and wrinkles. You will need other kinds of laser treatments for veins and hair.
Our clinic specializes in vein erasure. For the small veins on the face, we use pulsed dye lasers (PDL), intense pulsed light (IPL) and/or Nd:YAG lasers. These can treat both telangiectasias (red spider veins) and recticular (blue) veins. As for the facial hair, it can be removed with IPL. It will probably take several sessions to remove all of the hair. Be sure to consult a board-certified dermatologist who specializes in vein and hair removal.