That is a U-brake. The brake itself is mounted on a plate (that says "Tektro" in your picture).

You could, hypothetically, replace it with any other u-brake, but to what end? A single-pivot caliper brake may fit as well.

As above, you could replace the pads, as long as the arms move freely. Typically, u-brakes use different shoes than v-brakes (shorter and lower profile), but that doesn't mean you can't use v-brake pads. You need to either screw in the adjustment barrel on the lever (if it's unscrewed, that is) to create slack, or let some cable back through the pinch bolt. In a shop environment, I almost never adjust the brake with the barrel, only leaving it unscrewed about 2mm or so, so the owner can set the pull to their liking.