Since the speed of light is a constant, mass increases towards infinity as it approaches the speed of light, and time slows for the matter relative to matter wi

Since the speed of light is a constant, mass increases towards infinity as it approaches the speed of light, and time slows for the matter relative to matter with lesser velocity, does that mean that matter accelerating towards a black hole increases the mass in the region and further increases the magnitude of the effect on the spacetime curve? Is the mass of the black hole perpetually "falling" through spacetime at near the speed of light? Would the region around an "active" black hole appear more massive when it is consuming matter vs existing in a vacuum? A big object going really fast would be almost stopped in time, while at the same moment be almost infinitely massive which is increasing the gravitational effect. The combination of these effects is what makes such a big "dent" in spacetime?