Non-avian dinosaurs went extinct 65.5 million years ago, although birds are a direct continuation of Maniraptoran Theropods and are thus totally legitimate dinosaurs. Modern humans (Homo sapiens sapiens) in the sense of something that would be indistinguishable from us today appeared between 200 kya and 100 kya, depending on what you consider indistinguishable. I personally consider anything within the genus Homo to be human, which pushes humans back to 2.4 mya with H. habilis and H. rudolfensis (which could well be the same thing). So no, there is approximately 63 million years separating the end of the Cretaceous and the demise of all non-avian dinosaurs with the origins of humans.

Prehistoric humans often lived in caves because they were simple and effective means of shelter, but aside from that their remains are better preserved in caves and rock shelters than out in the open, which lends a bias to the material evidence. I don't know when the term 'caveman' came into use, but the popularization of the idea of the dimwitted ape-man came about when the first Neanderthal was discovered and recognized. Unfortunately the skeleton was of an old arthritic man, and the initial consensus was of a clumsy and primitive humanoid beast. Of course now we know this to be a grossly inaccurate and unfair depiction of our closest kin.

Edit: the Wikipedia article caveman addresses both of your questions. Apparently there was a film called The Cave Man made in 1912, which may be the earliest instance of the term being used, at least in popular culture. I suspect that The Flintstones and The Far Side comics actually did a lot to propagate the stereotype of the caveman in pop media.