Since the cold weather hit two days ago my hot and cold water faucets toward the back part of my home is not working, in the hot water only does not work in front bath tub of my home. The hot and cold water work in the kitchen.

Is the back part of your Home on the north side of you house? If so the water pipe supplying the faucet is probably frozen. And the rust is from a pipe in your water line being disturbed, probably from the freezing weather. The pipe should thaw soon after the weather gets above freezing for a few hours. There is a possibility that a pipe can be burst from the freezing weather.