As previously indicated, pslist will get you a task list on a remote computer.

To answer your next question, auditing file/program access, you will need to use the "Local Security Policy" in "Administrative Tools" (Win 2K and above), go to "Local Policies -> Audit Policy , and set "Audit Object Access" appropriately.

From the help text there:
Audit object accessComputer Configuration\Windows Settings\Security Settings\Local Policies\Audit Policy
Description
Determines whether to audit the event of a user accessing an object—for example, a file, folder, registry key, printer, and so forth—that has its own system access control list (SACL) specified....
Success audits generate an audit entry when a system event is executed ...

These audit events usually show up in the event log.

Disclaimer: I have not tried this out, so If it does not work, call Bill G...