That's what I saw, I've always equated Cardassia to Dostoevsky and by expansion Russia. The fatalism and the peace found in that fatalism is found in Russia and Cardassian culture I think.
I tend to feel very similar in the way I see the world, too. I don't have very much hope for the world that we see, but in contrast much hope and faith in God.
The Brothers Karamazov was a very interesting religious novel that wrestles with faith in a way I never saw in evangelicalism, that's my favorite of the ones I've read.
That is exactly why I like it--it tackles some of the toughest questions about faith rather than shying away or acting like the reader is stupid.
That is an excellent point about the Shakespeare vs Crime and Punishment which I'm sure Garak would have enjoyed. I suspect Bashir was keen to give him a Great Work that was also English where his family had their roots.
I've never been clear on exactly what country Bashir was supposed to have been from, though he definitely seems to have an affinity for English things.
As for Garak, I think he would have viciously mocked Crime and Punishment--yet on the other hand, perhaps been a little disturbed by a reflection of Cardassia, just by an author who came to different conclusions about what it all meant.