1) I haven't tried using an iframe for the file manager. I don't see why it wouldn't work.
2) This should be possible by using the sub-directory based on the session variable and by not showing the directory tree.
3) You can hand-code edits to the kfm files and probably accomplish this, but it isn't a supported feature.
4) I think it would work, but you'd have to try to be sure. It might take a small amount of tweaking, but since it uses a standard text field for passing data, it should be pretty easy to accomplish.
5) Under webassist/kfm/initialise.php you will find the denied file types on line120
6) You would probably want to copy the folder webassist/kfm/themes/webassist_v2 and name it for your new theme. Then update the template.html page to make design changes. Then update the design that is used from the webassist/kfm/filebrowse.js page on line 91, replacing webassist_v2 with your theme name.
7) You would probably have to do some hand-editing to get everything you are trying to do accomplished. It is possible, but not directly supported. I tried calling you to help you with some of these things over the phone but I got a voice mail.