Could a black hole swallow a star or galaxy?
Galaxies tend to me millions of times more massive than black holes though, so the separation and speed of all the stars within a galaxy means that a whole galaxy is not going to get pulled into a black hole!
Material from stars can, however, be pulled into a black hole. We can observe this when a star is in orbit around a black hole companion. The gravity of the black hole pulls (or "accretes") material from the surface of the star into the black hole, releasing enormous amounts of energy as it does so