1)   What is the dynamic here:  Does Saruman really wish to engage Gandalf and Theoden?  Would he have come out of his own will, or was he forced out by the command of Gandalf?

I believe he came out of his own free will and therefore assume that he did want to speak to Gandalf and Co.

2)  A few of you have briefly addressed this issue in your previous answers, but I’ll ask it so others can elaborate: Why does Gandalf ask Theoden to join him?  What does Theoden hope to achieve by confronting Saruman?

As many have already stated, this is the final "closure" of Saruman's bewitchment and control over Theoden.  Once free of any doubt, Theoden is then able to lead the Rohirrim to the aid of Gondor.  Gandalf is confident in Theoden's ability to withstand Saruman based on what the king has experienced and through the possession of Vilya.  Gandalf's presence there is crucial

3)  Realistically, what does Saruman think he can achieve by speaking with the King of Rohan?  Is he just trying to saving face in a bad situation? 

I'm not sure yet if he has completely burned his bridges with Sauron so any disruption in the ranks of Rohan would be seen as beneficial.  It didn't take him long to discover what Wormtongue threw out of the window.  I suspect he believed that his voice would have been sufficient to sway most, if not all, of the company, at least to leave the remnants of Isengard to Saruman.  As others have said, he underestimated the opposition.