There's some interesting stuff in the book The Genius of Dogs about how experiments that ascertained that dogs are able to follow the direction a humans points, proved that they are capable of more complex, independent thought than was previously believed.
Primates cannot follow human pointing unless domesticated/raised by humans, same with foxes and wolves cannot do it at all, but puppies of domesticated dogs can do it by 9 weeks old.
Nostress, my pup and I have very similar conversations and he's able to indicate whether he wants to go out, is hungry, wants water. I know when he wants something because he comes and sits directly in front of me and stares right at my face. Then I ask "What do you want?" and he stands up, then I go through the list "Are you hungry?/Do you want to go out? Do you want water?" etc and as soon as I say the right one he cocks his head on one side and heads to the appropriate location to wait for me.
As for things he's taught himself, most of them are just him responding to cues in his environment that he has noticed are consistent when something is about to happen eg, when I close the laptop I am usually about to remove my backside from the sofa, so he gets up and comes to see what I'm up to.
He has however taught himself to walk backwards a few paces so I can open the back door without bumping him and I have now put that on cue and find it useful in a surprising number of situations.
He had taught himself to use the kitchen bin as his personal food dispenser, but we've foiled that one now by buying a new metal pedal bin, as he really hates the clanging noise it makes.
While I was ill he did train my Mum to repeatedly get up and and close the back door, by coming and opening it then running off up the garden. You could see how funny he found his new game and knew to only try it with her, as no-one else would stand for it.
Lurcherboy, my older lad, is one of those dogs that knows when my husband has just left his office and is on his way home. I've checked several times and he's always right, despite dh having had three different jobs and using three different modes of transport including car, train and bicycle. He even knows when dh leaves head office in London, even though he won't be home for another couple of hours. Of course he's not that bright, because as soon as dh leaves Lurcherboy goes and sits by the living room door to wait for him, which is a bit daft if he's not going to be home for two hours. 
He always does the same thing - gets out of his bed, yawns, comes and puts his paw on my lap, wags his tail then goes to lie by the living room door. 