Yes, Einstein's theory of general relativity includes a theory of gravity. In fact, one of the main contributions of general relativity is a new understanding of gravity. In this theory, gravity is not a force between masses, but is instead a result of the curvature of spacetime caused by the presence of mass and energy. This curvature affects the motion of objects, causing them to follow curved paths that we interpret as being subject to a gravitational force. The theory of general relativity has been very successful in describing gravity in a wide range of situations, from the behavior of planets in the solar system to the properties of black holes and the large-scale structure of the universe.
No, the theory of general relativity does not disprove the existence of gravity, but rather provides a new understanding of what gravity is and how it works. While classical mechanics and Newton's law of gravitation treat gravity as a force that acts between two masses, general relativity describes gravity as a curvature of spacetime caused by the presence of mass and energy.
The effects of gravity can still be observed and measured in many different ways, from the motion of planets and moons to the behavior of light around massive objects. In fact, general relativity has been confirmed by numerous experiments and observations, and is widely considered to be the most accurate theory of gravity currently available.
So, while the nature of gravity is different in general relativity compared to classical mechanics, it does not disprove the existence of gravity. Instead, it provides a more comprehensive and accurate explanation of the phenomena we observe.