Not really. "Hebrew" certainly WAS derogatory, derived from the ancient Egyptian he biru, "cave man". "Jew" needn't be, it depends on the manner in which it's said.
No. My Jewish friends have always referred to themselves that way. I also wrote for a JCC and used the word and they didn't edit it out, so I'm pretty sure it's ok. If I ever happen to come across someone who is offended by it, I'll certainly correct course, but as far as I know, it's ok.