Hiya,
You are right to use the Ajax Spider instead of the standard one, as your site makes a lot of use of JavaScript.
However its always much easier to configure ZAP to handle authentication manually rather than going straight into automation.
Although it focusses on form based authentication the general principals are the same.
Proxy your browser through ZAP so that you can test authentication without having to launch the ajax spider.
Follow the Diagnosing Problems section and if you cant work out whats going on then follow up on this thread.
Re the session management - how is your application managing the session? ZAP will need to understand this, and if you dont know how it works then you wont be able to configure ZAP to understand it :)
Cheers,
Simon