In The Lord of the Rings: The Two Towers, was Saruman aware of the Ents' existence when he was cutting them down and using them for fuel?
I don't think it's specifically mentioned in the Theatrical versions of the movie. However Treebeard does talk about Saruman, saying:
There was a time when Saruman would walk in my woods. But now he has a mind of metal and wheels. He no longer cares for growing things.
Saruman is a Maia, essentially a divine being, vastly more knowledgable and long lived than people, and Gandalf's superior, as leader of his order but also in power and knowledge. Saruman also lived in close proximity to Fangorn Forest. It seems extremely likely that he would be aware of the Ents.
[In the books it is much more explicitly stated that Saruman and Treebeard are aware of each other]
It's almost certain. Based on what we know:
- Ents are of the First Age and Treebeard, called by Gandalf the oldest living Ent and the oldest living thing that walks in Middle-earth.
- Saruman //snipped// was an Istar (wizard), who lived in Middle-earth during the Third Age... //further down the page// Leaving Isengard undefended resulted in its destruction at the hands of the Ents (Saruman had underestimated the Ents' anger and strength).
Plus, Saruman was Gandalf's tutor, so he was likely the person that told Gandalf about the Ents in the first place.