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Its mass can be measured just like any other object. We can't see a black hole, but we can see things around it and how they are affected, and using physics determine what mass would be needed. If the Sun magically became a black hole, it would have the same mass and the planets would orbit the same. So we could measure how they go around it and come up with the mass at the center.
One way (I believe) to measure a black hole indirectly is to see how it bends light images from things behind it. Same thing, we can calculate how much mass would be needed to bend that image's light path.
The second question, a star can pull a black hole, it's just a matter of the two masses. Usually you'll find the black hole is much larger, but in theory a small black hole could orbit a large star.