Yes, it should auto switch from Internal to Headphone and vise versa if headphone is inserted and remove.
The kextcache log and IOReg file you attached in the debug file shows no existence of CodecCommander.kext.
Google for the kext and install it to /Library/Extensions
Repair permissions and rebuild cache.
If that still doesn't work, change the layout-id in Config file under devices/properties from 12 to 18.
No, as you can see in your system information under display, you'll see both graphics. It's also showing in your IOReg file.
Try adding boot arg -wegnoegpu to Config file
If that doesn't work, we'll need to disable it via DSDT/SSDT patching