Ranger, dwarf, and elf are spooked. And for various reasons, 'ranger' does get its own label rather than just 'human'. That Aragorn, as a human, has more vaunted tracking skills than the elf, speaks volumes as to the abilities of the Númenóreans. Between their various skills, they do a decent job of CSI: Middle Earth, and put together a decent reconstruction of the previous events.
Even the dwarf picks up on the... awareness of the forest. Again, Legolas as a wood elf has not the familiarity to identify the true nature of the Fanghorn, but does have enough to recognize the nature of it. We get a gentle reminder of the life spans of elves, even a younger one like Legolas. Fanghorn is enough to make Legolas feel young, while he is old enough to consider Gimili and Aragorn (the elder of the two) 'children.'
I'm not sure about the direct use of "Treebeard's Hill." As a story told in third-person, Tolkien has the ability to reference things that the present parties have no knowledge of. The mention itself both makes sense and breaks the scene for me.
With both known fact and rumors, their assumption of Saruman's presence is the logical one. Part of me wants to say that even had they not stayed their hand on chance of innocence, that they would have little luck taking on Saruman. But the power of the Wizards rarely seems that of direct martial confrontation. They have powers, but even with Saruman do we rarely see direct displays, rather we see their knowledge, cunning, and manipulation of individuals and events. That being said, if it was Saruman I'm pretty sure letting him talk would be the worst thing they could do. Fortunately, they met instead an old friend (and just as fortunately, one who is more than capable of defending himself).
Tolkien and Jackson went about building up tension to this reveal in similar ways, playing up on the ignorance of the party. They've chosen to drop misleading hints in different ways, with Jackson cutting out many of the references to Saruman's suspected mischief (and giving us explicit rabble-rousing) and giving most of the leading hints to the scene with Merry, Pippin, and Treebeard. Aragorn, Legolas, and Gimli are equally concerned about the threat of the White Wizard, but less concerned with attacking what could be just an unknown threat. Jackson goes so far as to distort Ian McKellen's voice such that it sounds like Christopher Lee's (possibly an actual blending of their voices), before revealing his face.
The importance of names and identity come up here. Gandalf isn't necessarily "Gandalf" anymore, though he is willing to answer to that name. He even goes on to say "Indeed I am Saruman, one might almost say, Saruman as he should have been." He doesn't claim any name, simply acknowledges labels that apply. The label Gandalf stands as good as any, especially as he is willing to to answer to it. But we need to keep in mind that he is not the same person, even if he has mostly the same memories and goals.