I am going away for a few days and although I don't want to prevent my kids from deleting files while I'm gone, I want to prevent them from being able to empty the recycle bin. I want to check what was deleted when I get back in case an important file was deleted by mistake. Is there a way to allow deleting files but to restrict the "empty recycle bin" action in Windows 7 Ultimate?
You can remove it from the Desktop. On Win7 go to Start > Control Panel > Appearance and Personalization > Personalization > Change Desktop Icons. Once there, uncheck the box next to Recycle Bin and hit Apply. That should keep most people away from it. The Recycle Bin will still show up under the Desktop in the File Explorer however so depending on how savvy your kids are, they could still get to it.
This also doesn't prevent them from doing Shift+Del to directly delete the file, bypassing the Recycle Bin entirely.