Does my Schlage BE365-CAM BE365CAM505 have a feature that allows it to automatically lock the deadbolt without having to enter code and turn the dial?

Sort of. The lock has what is called the "turnlock" feature. When enabled, you have to only push the Schlage button, then manually turn the "dial". When disabled, you have to enter the user code, then turn the dial. So either way, you still have to turn the dial.

To enable/disable this feature, enter your Programming Code --press Schlage button--press 7

Each time you do this, you toggle between enabled and disabled.

"How can I program my electronic keypad lock when the instructions with the Programming Code have been lost?"
The back plate of the keypad side of the lock on the exterior of the door has a sticker which includes the serial number, six digit programming code and two pre-programmed four digit user codes. The lock must be disassembled to a point the exterior of the lock can be pulled away from the door and the information on the sticker made note of.

Complete installation & programming instructions can be found here:

http://consumer.schlage.com/Project%20Documents/P515-858.pdf

Notice that the above is a .pdf filetype. That means that you need to have Adobe Reader or similar installed on your computer to view it. So if you are unable to view the file, download (for free) and install Adobe Reader first. You can get it here:

http://get.adobe.com/reader/

Videos for installing and programming can be found on this page:

http://consumer.schlage.com/Service-Support/Pages/InstructionandManuals.aspx

Scroll down and find them under the heading Electronic Security-Keypad Deadbolt BE365

Good luck!