No, you cannot restore AD from 2003 to 2008 directly. You need to upgrade the AD infrastructure to 2008 (schema update).
no it is not possible if you need to restore the 2003 will be restored only on windows 2k3 OS and same is with the 2k8
Active Directory Recycle Bin helps minimize directory service downtime by enhancing your ability to preserve and restore accidentally deleted Active Directory objects without restoring Active Directory data from backups.By default, Active Directory Recycle Bin in Windows Server 2008 R2 is disabled. To enable Active Directory Recycle Bin, your environment must meet the requirements to completed scenarioused to restore object deleted form AD or restore Multi OUs.
Repair or recover Active Directory.
Active Directory was previewed in 1999, released first with Windows 2000 Server edition, and revised to extend functionality and improve administration in Windows Server 2003. Additional improvements were made in Windows Server 2003 R2. Active Directory was refined further in Windows Server 2008 and Windows Server 2008 R2 and was renamed Active Directory Domain Services. Active Directory was called NTDS (NT Directory Service) in older Microsoft documents. This name can still be seen in some Active Directory binaries.
In Windows Server 2011 it is called Active Directory.
Directory Services Restore Mode
Active Directory
Directory Services Restore Mode (DSRM)tryrestartable Active Directory feature, which allows you to place the ndts.dit file in a offline mode without rebooting the domain controller outright.
Some books one could use as tutorials for Active Directory are Active Directory Cookbook, Active Directory for Dummies as well as Windows 2000 Active Directory. All have various problem solving techniques one could use and they can be easily referenced.
The following changes are available in Windows Server 2008 R2:Active Directory Recycle Bin Active Directory module for Windows PowerShell and Windows PowerShell™ cmdletsActive Directory Administrative CenterActive Directory Best Practices AnalyzerActive Directory Web ServicesAuthentication mechanism assuranceOffline domain joinManaged Service AccountsActive Directory Management PackBridgehead Server Selection
Active Directory was previewed in 1999, released first with Windows 2000 Server edition
Active Directory on a Windows Server 2003 Networkhttp://technet.microsoft.com/en-us/library/cc780036.aspx