How can radiometric dating of meteorites determine the age of the earth? Wouldn't this only determine the age of the decaying nuclide in each rock?
Many of your questions are answered in this question and associated answers:

Why is Earth&#39;s age given by dating meteorites rather than its own rocks?

To add to some of your other questions:


  Wouldn't radioactive decay have already been occurring in all of those meteorites long before they hit earth or our moon?


Yes. We have an assumption that the Earth formed at about the same time as the meteorites. The age obtained for meteorites is not the time when they hit the Earth, it is the time when they formed. Which is reasonably assumed to be close to the age of the Earth.


  Wouldn't this only give us a lower bound on the earth's age? How do we know there doesn't exist some older meteorite out there indicating the earth is older then 4.5 billion years?


Because we haven't found one. We have found thousands of meteorites and none have an age older than that. Yea, there could be something that we simply having found. But the more you look, the more a pattern emerges.
Furthermore, there are other systems like 26 Mg-Al which do not date how long ago things formed, but rather how soon after the supernova things formed. This allows us to know that meteorites that formed 4.5 billion years ago, also formed within a few million of years after the supernova that made the nebula and all materials in the solar system. Therefore, Earth could not be older than 4.5 billion years.



Al-26 forms abundantly in supernovae and is radioactive with a half-life of almost a million years. Minerals which contain both Mg and Al (such as spinel: MgAl2O4) will initially incorporate Al-26 which will then decay to stable Mg-26. When measured, the mineral will have an excess of Mg-26 relative to what is expected, and then it can constrain its formation time to the time when Al-26 was still around (without a few million of the supernova). The same meteorite can then be dated using other methods (usually U-Pb) to determine how long ago it formed, and the answer is usually ~4.5 billion years.