Did cavemen really exist?

Yes. The term cavemen refers to ancient humans in Europe who used caves or rock shelters as their primary place of living.

I think the term "cavemen" is a bit of a misnomer. Yes, there is evidence some ancient humans lived in caves. There is also a ton of evidence to indicate ancient men were smart enough to realize when it got too cold or wet to "sit it out" under a tree, one watched and copied what the animals did.: Dig a Burrow, or build a Shelter! Since some shelters assembled with ease, it became easy to teach others to build the same thing. As shelters became portable, man discovered he could migrate with the herds he hunted.

Did cavemen live with the dinosaurs? Not likely. The best evidence indicates the dinosaurs died off about 45 Million years before the first proto-hominids. (Mammals which, with a lot of imagination, resemble humans.)

Yes - they left lots of bones - and some really neat paintings.