With reference to this clip, Gandalf revealed his identity to the Balrog and fended him off with his own powers. Considering that, as Istari, he usually made sure not to reveal his true nature to anyone, did anyone in the Fellowship understand the true significance of what is revealed to them as they watched and heard Gandalf standing up to the Balrog?
Edit: Also, when Gimli and Legolas bowed before Gandalf the White in that clip, what is the reason? Did they bow because he is Gandalf, or is it because, as I asked, they have realised what he is?