How would Freud analyze Nora from A Doll's House?How does she fit into his theories?

I think in order to address such a question, you would have to examine how Freud looks at civilization and its compulsion to force us, as human beings, into roles that we might not want to play.  The idea here is that there is a factor of sublimation that causes an internal conflict within all human beings between what we want and what we have to do, the person we wish to be and the person we have to be in order to be accepted by social constructs.

After this, I think you can examine how women, especially Nora, fall into this conception.  Are there situations where she has to fulfill conditions that are dictated by social settings?  In other words, must she sublimate her desires to social conventions?  The answer is obvious, but finding evidence will help your case.  Thus, Freud might see Nora as representative of how society treats all of us, especially women.

Final point.  The battle of society's control over our true identities might be extrapolated into Freud's closing lines of the battle between eros and thanatos.  This battle between love and its counterveiling force might be played out in Nora's establishment of her own voice at the end of the play.  Perhaps, this could be Freud's hopeful vision of eros conquering over thanatos.