I have recently heard of the notion that Samson and his story had roots in older stories and these same stories also started Hercules and that they are both based on myths. Is there any source to this and if so, does this mean that the Tanach has myths in them meaning it is false. Thank you.
No, there is no source that shows the story of Samson to have come from the story of Heracles or some proto story which preceded them.
There are scholars of mythology who may try to find similarities between the stories of one culture and the next. However, any such similarities do not show or prove that one story came from the other one. This is because those similarities are subjective at best and usually forced.
Obviously, there may be exceptions, but we would only assume two stories shared a common source when multiple details of a peculiar sort matched each other in each story.
I have read both the story of Samson and the story of Heracles and the only similarity that seems to be a simple comparison is that both characters defeated a lion.
However, Bellerophon is a mythical character who preceded Heracles and did battle with the Chimera which was a beast with the head of a lion (albeit the body of a goat etc.). Enkidu of Akkadian mythology in the Epic of Gilgamesh; (according to some scholars) is depicted as a Bull-Man who is fighting with a lion.
The Tanach even tells us that King David killed a lion as a young shepherd (and a bear). However, no one claims that the King David story "copied" the Samson story.
Rather, many world cultures realized that lions are powerful creatures and if any culture would spin a yarn about a hero, it is in all likelihood common, to see a chapter in the hero's story, depict the hero as slaying a strong and dangerous beast like a lion.
So if two stories have scenes where the hero slays a lion, it would force absolutely nothing as far as suggesting a common origin or "borrowing" from one culture to the next. Why would a culture borrow such a story when they can easily make it up themselves!?
Other than that though, the two stories of Samson and Heracles have no substantial similarities.
The Tanach has been passed down to us in word for word format from our nation as a whole by the Prophets and spiritual leaders and common masses of Israel. The words have not been changed.
Also, the story mentions Samson's real life father by name and his mother, as well as their residence and tribe, in a specific timeframe of history. Many historical details also appear in the story.
There is really no reason to believe that the historical account presented and preserved, by a nation to its children for thousands of years, should be some fake myth.
In other words, just suggesting so doesn't make it so. The burden of proof to say that the story is myth or borrowed, rests upon the one asserting that it is a myth.
So no, the Tanach does not contain myth or falsehood. The Jewish people safely relies on their solid Masorah (tradition).