You'll have to clarify a bit, that doesn't make sense to me. How can a thinking social animal not be aware of it's own existence?
This is a little weird. What makes you think a dog doesn't know what itself is doing at any given time? Playing is a perfect example because it serves very little genetic, food drive, or evolutionary function. They do it precisely because like us, they have complex brains, a sense of self, and get bored.
If that were the case and the brain controlled the animal instead of the other way around, how could each animal be so unique in it's personality, taste in food, temperament, etc. I really am curious to understand why you insist they are so simple. It seems extremely obvious to me that they are at core really not that simple, each is entirely unique. Of course, the species shares it's genetic goals. Survival, sex, and status. Then again, at core, that's exactly what humans are after as a species as well. What makes us different from one another is our complex brains and personalities that go with them.
Of course they do. Envy is a basic component of any social animal, especially a pack mentality driven animal. They literally understand where they are personally within the pack. They know which members have better standing and envy the benefits of that standing. Envy itself is a very complex emotion, and many times even humans don't realize how envious they're being... It's what our brains tell us to do. Covet a better situation.
Here's a study article with some interesting findings, including controls.
http://www.livescience.com/3124-dogs-feel-envy.html
The tests performed showed rather clearly that the dogs outright knew when the other dog was getting a better reward for the same action, and it upset them visibly, even to the point where they made the decision to stop performing the act and changing behavior towards the other dog out of jealousy.
I'm still curious what evidence supports this theory. How would it benefit any complex brain animal to not understand what it's doing and what it's current goals are?