When you deal with HR stuff, you start skating on thin ice. HR information can be extremely touchy, especially since many HR departments in the US also handle Worker's Comp claims, which fall under HIPAA regulartions. HIPAA has its own set of security requirements which just changed recently.
If you are buying a commercially available system, then you need to consult with your vendor on this information. If you are building your own system, your HR director and attorney need to be consulted to find out what legal requirements there are on the types of documents you are handling. Those requirments will need to be reflected in your system.
HAVE AN ESTABLISHED SECURITY POLICY AND ENFORCE IT RELIGIOUSLY.
Dealing with highly confidential information is a touchy issue and, frankly, most companies don't get anywhere near the level of security needed to protect that kind of information. I have worked with many document management packages as well, and I have yet to find any that provide even the most basic level of security, IMO.
To address your specific questions, I will try to use our security policy for examples.
How many system administrators are there who have full access to the information?
As few as possible, but never less than two. Don't put all your trust in any one employee, but don't give away the farm, either. Operate under the principle of lowest priviledge, even with admins. Make sure that your admins are qualified and trrustworthy enough to trust with such data.
Are the admins business users or IT or some of both?
That depends on the administrative task. Resetting passwords and adding/removing users are functions that the HR Director has, but not the level of authority that could break the system.
What kind of reports, alerts or other controls are there to notify system owners, administrators or other data owners that someone has viewed, downloaded or otherwise accessed information they should not have access to?
Two words: Full Auditing. Nothing happens on the system that isn't recorded. All data access is handled by stored procedures which log information about: who accessed the data and when; what, if any, changes were made; and what the previous values were when they were changed. A random sampling of the log is checked to ensure nobody is abusing their priviledges.
How is communication handled?
I'm not sure what kind of communication you are referring to. Are you asking how communication takes place between the front and back ends of the system, or between users?