Well, despite your stated concerns about ProLogic, it appears your DirecTV box is working correctly in that PLII is not available when playing HD content, which has DD 5.1 audio. Why do you think your sound system is not reading the audio correctly? Plus, if the option to engage PLII also disappears after a few minutes when playing your AppleTV, it may be working properly, too. Presumably, your receiver will show you the format of the audio it is getting, which would clear this right up.
As for your AVR turning on and switching to wrong input, I suggest you turn off Consumer Electronic Control (or whatever Samsung calls it) and see if that fixes the problem. CEC can produce unexpected results. While ARC is convenient, you get the exact same audio using an old fashioned digital connection without any of the flakiness of CEC.
btw, I have never heard of DTS NEO 2.5, the format you listed for the TV audio output. Neo:6 is the DTS version of ProLogic and it is not discrete 5.1. Your TV output needs to DD 5.1 if you want to get surround sound.