Bored to death is an expression, and sounds fine to me. The other two sound a bit strange, people would understand what you meant but they're not really things people would say. You can also say "bored to tears" if you want.

Hey, Ppman! Normally this "to death" usage comes after an action. In your examples it would be: 1. I am burning to death 2. (This sounds correct) 3. I am starving to death (Which means that starving is so much more than to be hungry, for you to use the metaphor). Anyway, I believe that the examples are grammatically correct. I hope this helps!

If it's very hot you could say: This heat is killing me. I’m dying in this heat. And if you're extremely hungry you could say: I’m starving.

No. Only 'bored to death'. The others don't work at all, I'm afraid.

No, you can't translate ___死了 into English like this in every situation, as it sounds really weird, but you can in some cases. I'm bored to death, for example sounds OK. It's best to learn from context. Laurence.