There isn't really an answer to your first question, I'm afraid (although note that this is at the limit of my understanding, and someone may correct me). In General Relativity, gravity is not a force. Mass changes the definition of "straight line" so that objects moving freely tend to curve toward it. The maths describing that is rather complicated, but you find that you can recover Newton's gravity-is-a-force maths if the gravity is weak. However, gravity is not weak near a black hole and it isn't really possible to treat that kind of thing as a force in a coherent way.
All mass distorts spacetime. That's what gravity is, to the best of our knowledge. Under some circumstances you can pretend that Newton was right because the maths is a lot simpler and the errors are too small to matter. For example, NASA throws spacecraft at the outer planets without Einstein. On the other hand, the GPS would report wrong positions if it did not allow for spacetime curvature.
Finally, there is no known limit to the range of gravity. Given enough time, any mass will pull you in unless you do something like orbit it. If you are far enough away, though, nearby sources of gravity will dominate - for example the Earth's gravity is much more important to you than that of a supermassive black hole two galaxies over.