Revelation 21:4: I do not think this is referring to the healing of saints. To me, it is a great summary statement: the power of death and suffering is now over (1Co 15:54)—finally Death is swallowed up in victory! The shortest verse of the NT, "Jesus wept" is found in John 11. He was to be sure weeping for his friend Lazarus, but also I think for death itself and its power over creation. In Rev. 21:4 now the curse, the Fall and its effects are over. And now God Himself will wipe every tear! And the other effects of the curse are now over as well.
Revelation 22:2 "the healing of the nations": The term "the nations" is a sometimes catch phrase for people who are not Jewish. The movement from salvation for the Jewish people only, to salvation through the Jewish people to the Gentiles (all the rest of "the nations") is one of the great themes and movements of the New Testament. A careful reading of the entire Gospel of Matthew shows this movement, culminating in the Great Commissison (Mt. 28:19-20). Is this healing of the nations the practice of medicine as we commonly call it? Or, is it a colorful way to say, "the salvation?" I suggest that even though this is the Greek word therapeia, it may well mean "salvation"; another common word for "salvation" (sozo) can mean either "healing" or it could mean spiritual "salvation." My sense here is that this is what John is doing. John's Greek in Revelation is well known as being not as refined or regular as the other NT Gospel writers.
When I read Revelation 21-22, I am reading the "rest of the story". The beginning of the story is found in Genesis chpts. 1-3. Finally, all the wrongs in the first garden are being made right in the final garden.