How can I tell the OT of the Bible is the real OT (ie the original Hebrew
Bible) or if it is really just a more modern day Jewish OT? They claim the
Bible’s OT is rewritten and has mistakes. Can you please clear things up
for me?

I believe I give a pretty thorough answer to this in an article found at
this web site-
“HOW WE GOT THE BIBLE”.

You will find the material relevant to your question in the second half of
this article. In a very small nutshell, given the evidence of he
Septuagint Greek translation of the entire Old Testament in the period
250-150 BCE and given the Dead Sea Scrolls, which have entire Old
Testament books and at least fragments of almost every Old Testament book
in Hebrew from the 200-50 BCE time frame, one can say with confidence that
we definitely do not have some sort of modern Jewish Bible which has been
changed significantly from the original.

However, given the imperfections of copyists, one can assume that we do
not have a perfect original of the Hebrew Old Testament. The evidence
points to a reasonable assumption that the Old Testament has not been
extensively rewritten from the originals. However, it would be fair to say
that there are a significant number of small errors which crept into the
text of our Hebrew Old Testament through copyists errors and possibly even
minor attempts of scribes to “improve” the original.

I would suggest as a supplemental book, How We Got the Bible, by Neil R.
Lightfoot (Baker Book House, 1988)

John Oakes, PhD