Actually the New Testament is a product of what we now call Western Civilization.
The Tanakh, which Christians call the Old Testament, is actually a product of Eastern thought. Even the Jewish exegesis of it is far different than what is claimed by Christians...
1. The Scriptures are scientifically accurate.
Not in the eyes of Jews. The Scriptures are not the basis for our religion or culture, but a product of these two things. They reflect ancient ways of thinking, employ old and unscientific cosmogonies, even its views on G-d are ancient and primitive when compared with modern Jewish thought,
2. If the Bible is flawed, G-d is flawed.
Again, a Christian thought. The G-d of Abraham and Sarah is not perfect in the way Christians demand and define perfection. In Jewish theology and Scripture G-d is evolving with humanity and learns how to love properly and deal more justly through interchange with humanity. In Judaism it is not wrong to say that it seems G-d created humanity to fill a need in order to move beyond what was lacking in the Creator.
3. Abrahamic Faith
Faith and belief are irrelevant concepts to Jews. We don't "believe" in G-d in any manner similar to Christians who believe it is a requisite to have faith in G-d's existence. Instead G-d is encountered, responded to, interacted with, even challenged. There is no such thing as the "Abrahamic faith." Jews are in a covenant with G-d, and this leaves some of them in active participation with the Creator and others guessing at G-d as agnostics and other Jews dealing with the G-d concept as atheists. But each Jew still remains part of the Tribe, and each can still fully participate in its rich spiritual tradition, theology, and work together to fulfill the aims of Tikklun Olam.
4. Truth is found in written texts.
That is too limited a concept for the children of Abraham and Sarah. Truth can be found where we least expect it. Even the Hebrew Scriptures are not the basis of religious truth, as our "truth" existed for centuries before we wrote them down as Scripture. Our religion was totally functioning with a theology and Temple before Scripture was complete. In fact Scripture was an afterthought, not the beginning for us.
So yes, one can probably find many truths from sources like the Vedas. But you may need to revise your views about the Scriptures of the Hebrews. They are tied to a very foreign theology that many Christians are still ignorant of after 2000 years. Some of your comments about them are in need of a bit revision.