1) My first question deals with the original LXX. I understand that it was completed around the 3rd century B.C. However, what happened to the original documents? Was the LXX lost or destroyed sometime? Was it copied? If so, what was the name of this copy?
I think, perhaps, you have to readjust the way you think about ancient documents in general. We don't have the originals of any
piece of ancient literature. Not Homer. Not Plato. Not the Hebrew Bible. Not the Septuagint. Not Cicero, Galen, or Ovid. Not the NT. Not the writings of the Fathers, etc.
What do we have? Take the Septuagint as an example. We have three major sources:
1) A variety of manuscripts. These are handwritten copies -- actually, usually copies of copies of copies. Some manuscripts were copied early on. Some much later on (100s, even a 1000 years later). Some are complete. Some are only fragments.
2) Quotes in other sources. For example, the NT itself and the Church Fathers often quote from the Septuagint. Thus, we can compare their quotes to the text found in the various manuscripts.
3) Translations into other languages. For example, there are relatively early translations of the Septuagint into Latin and Coptic. Occasionally, the translations help clarify certain passages. Also, there are certain ancient writings, e.g. St. Irenaeus, that only exist in a translation other than the original.
2) I keep hearing how the Septuagint was a translation of the original Hebrew scriptures AND THEN I read how there are English translations of the Septuagint. However, after further research I am finding that there is no English translation of the original LXX/Septuagint. So my next question is, what are all of the documents that we know of that are considered a 'Septuagint' today? (i.e. Codex Vaticanus, Sinaiticus, etc.)
Depends on whom you ask. The Septuagint has an extremely complicated manuscript history. Vaticanus and Sinaiticus are two of the best versions.
One of the major scholarly disciplines is producing what is called a "critical text." That requires assembling all of the different versions, manuscripts, quotations, fragments, etc., and trying to figure out, word by word and phrase by phrase, which one is the oldest in that particular case. There is a whole science behind this process, but it is still only a theoretical reconstruction.
Some German scholars have been doing that with the Septuagint. It is called the Göttingen edition. Cambridge published an edition of Vaticanus that also includes some references to other manuscripts.
4) Of the known 'Septuagints' which one is considered the most reliable or true to the original Septuagint?
Vaticanus or Sinaiticus.