Not a real answer, but some hints.
If the HtmlUnit stores cookies in memory then Will HtmlUnit respond the server with cookies?
HtmlUnit's cookie policy is to be browser-compatible so I would expect it to do so.
When the HtmlUnit session terminates? Will it terminate when i call webclient.closeWindow()?
I'm not sure about this one. Did you try to test or debug this? Did you look at the source code? Actually, I wonder what should be the expected behavior here.
As acc. to the HtmlUnit docs, WebClient represents a browser, so does it represent a mutiple-windows browser (like IE7 in which we can open multiple tabs) or a single-window browser?
I consider that WebClient represents a single tabbed browser.
If it represents a multiple-window browser, then does the HttpSession is maintained accross multiple windows of that webclient like real browsers?
Note that this behavior is not consistent between browsers and between browser versions: IE6, IE7, IE8, Firefox, Chrome, they all behave (more or less) differently (see Cookies in Firefox and Internet Explorer, or Browsers, processes, cookies and session state, or Session Cookies, sessionStorage, and IE8). So I wouldn't consider that there is a general rule with "real" browsers.
Actually, I think that your best weapons are the source code and your debugger. These questions would be easy to verify IMO.