Difficult to mine? Maybe if you're still using the antler pickaxe they start you with. Upgrade to a bronze pick asap to help make further mining easier.

As for rare? Nah, it's all over the place in the Black Forest. You just need to get good at spotting it and you'll see a node practically every hundred feet. And note that the majority of a copper node is underground, so dig around the entire outside to reveal it and give yourself a definitive area to work in.

No, they do not respawn, but it shouldn't be an issue with how plentiful they are.