Not sure about the older models, but in my 2014 Diesel when I come to a stop light, the transmission falls into a neutral state to act as a fuel saver. This is how it's supposed to behave and is mentioned in the manual. That sort of seems like what you're experiencing in your last point. As for the others, there is a lot of talk around here about transmission fluid type and which to use for best performance. When is the last time it was changed? What was used? Did you check recently to make sure it isn't low?