How do I know what rules or monitors are running on an agent?

Operations Manager console
If you look in the monitoring view, operations manager, agent, agent health state dashboard. Select your server under Agent State and there is a task \ action on the right of the screen to show running rules and monitors for the health service.

Reporting
> Generic Reports > Management Packs

Powershell:
Get-managementpack | format-table Displayname,Version | export-csv c:\installedmp.csv

SQL:
SELECT MPName, MPFriendlyName, MPVersion, MPIsSealed
FROM ManagementPack WITH(NOLOCK)
ORDER BY MPName

Agent:
> When an agent receives the MP, an event 1201 is logged to the Operations Manager log on the agent. The event includes the name and version of the MP that was received.

> When the changes have been applied, an event 1210 is logged on the agent, indicating the new configuration is now active.

> In the agent installation directory (c:\program files\system center operations manager 2007\ by default), you will find a \Health Service State\ManagementPacks\ subdirectory. In this directory, you will see copies of the management packs received. Simply by watching the “Date Modified” column (in detail view), you can see when an updated copy was last written to the file system.

You can also download the Effective Configuration Viewer although the information provided isn’t accurate on R2:
http://www.microsoft.com/downloads/details.aspx?FamilyID=A9DB4DCA-6716-478D-89B9-42F27EBC76A8&displaylang=en

What rules or monitors are in each Management Pack?

Check out OpsManJam …
http://www.opsmanjam.com/OpsManJam%20Library/Forms/AllItems.aspx?RootFolder=%2fOpsManJam%20Library%2fMPViewer%20Dumps&FolderCTID=&View={C9321DFE-CF3E-4F57-8873-3D4C1F6609F4}