If you have your own domain, you can install the opensource Moodle LMS and it will allow you to do everything you've listed and much, much, more. Plus as the administrator, you will have full control over the functionality of the site.
If you don't have your own domain, you can still get access to moodle through http://www.e-socrates.org/ - I haven't used this service so I can't comment on their response time, etc.
These two leads should get you started... for now;
You should try http://enterthegroup.com, it has;
*private group/personal pages
*file sharing and more
and it's also free