Trying to include WordPress within a main container

I’m new to WordPress and attempting to include it (through AJAX) into a main container <div> on my site. I’m currently trying the WikiWP theme.

The situations I’m facing are:

1) When logging-in to WordPress, the login page doesn’t stay within the container <div>. A new web page is generated instead.

2) When WordPress sees me as ‘logged-in’, it places the admin toolbar at the top of the browser window (again, outside the container <div>).

Does anyone know of any way to keep WordPress completely within an ALAX-specified <div> ??

Thanks !!