I would put it in the subjunctive form: "Do you wish that I were dead?" But many English speakers would use "was", so it's not that important to learn the subjunctive "were". "Would you like me to be dead sounds odd, but Callum's suggestion is a good substitution (although again, I'd tend to use the subjunctive "were").

The second one is the more natural expression.

Because the first option starts with "would you like," it kind of sounds like it's an option that someone can choose. Like an offer. So, if I were to read that or hear that, I would assume there is a background story where this person being dead is probable. The second one is a natural expression we tend to say when we feel like someone just really doesn't appreciate us and couldn't care less if we were dead. Sheesh.

Not exactly interchangeable, no. It would be closer to being interchangeable if the first sentence was: "Would you like it if I was dead?"