The fossil evidence does indeed support a bird-dinosaur relationship. In fact, it's a done deal, and I'd argue that birds are dinosaurs, in the same way that humans are mammals. However, feathers are not derived from scales, although there's a close relationship between the two.
And although the bones in the leg of a T-rex are arranged in an almost identical fashion to those of a pigeon, the T-rex walked differently, mainly because the tyrannosaur had a long, muscular tail. Living birds have a different center of balance.