1)  Theoden says he’s worried about his faltering feet, but of more concern is the potential for his mind to falter.  Does Theoden possess the strength of will to successfully confront Saruman alone? If Gandalf had not been there, would things have gone differently?  Was Gandalf actually doing anything to aid Theoden? 

Well, Théoden's reply to Saruman indicates that he could have done it alone, but he is a mortal man standing up to a wizard, and the fact that he was once under Saruman's control could make him more vulnerable. I'm glad that Gandalf was there to support him, although I don't think Gandalf did anything other than to provide moral support and show solidarity.

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Although now long estranged, Man is not wholly lost nor wholly changed.
Dis-graced he may be, yet is not de-throned,
and keeps the rags of lordship once he owned:
Man, Sub-creator, the refracted Light
through whom is splintered from a single White
to many hues, and endlessly combined
in living shpes that move from mind to mind.
Though all the crannies of the world we filled
with Elves and Goblins, though we dared to build
Gods and their houses out of dark and light,
and sowed the seed of dragons--'twas our right
(used or misused). That right has not decayed:
We make still by the law in which we're made!