The original language of the OT is either Hebrew or Aramaic for most books, while in the NT the majority books were probably in Greek. My question is, do we still have the Hebrew Genesis for example, that is though to be the same as the original Genesis written by Moses? Do we still have the Greek version of the Gospel of John for example, that is thought to be the same as the original?
If you mean, do we still have the original manuscripts, of course no.
There is no ancient work that has the number and quality of manuscripts that the bible has. Critical editions have been published that give us the genuine text of the bible. There are certainly minor changes from the original, but they would be few and far between,.
It is good that you asked that because it is surprising that many people assume that if a Biblical book is in the original language that it must be original. Even St. Jerome erred a bit when he assumed that the Hebrew text of the Jews was the “Hebrew truth”. All the manuscripts show us that there are different manuscript traditions. I personally believe that the authors wrote more than one copy and some wrote the same thing in more than one language, and therefore there are more than just one original.
The oldest surviving fragments of the Old Testament are the Dead Sea Scrolls, which still date to hundreds of years after the originals were written, from about 150 BC to 70 AD. The oldest mostly complete New Testaments we have are the Codex Vaticanus and the Codex Sinaiticus, which date to about the fourth century. There are a few small fragments of the New Testament that exist that are slightly older, with the oldest fragment of any kind dating to the second century.