Yet implies something will probably happen in the future, but has not happened when the speaker is speaking. So, you are correct re: the letter example. Re: the rain example, we all know that when it rains, it will eventually stop. So, if it is still raining, one might say "It is yet to stop raining." Or, one might ask, "Has it stopped raining yet?" Or: "Has it stopped raining? "No, not yet."