Metacognition is defined by Merriam-Webster as:
Awareness or analysis of one's own learning or thinking processes.
The above Wiki link provides as a couple of examples:
A person is engaging in metacognition if he notices that he is having more trouble learning A than B; [or] if it strikes him that he should double-check C before accepting it as fact.
So you might be misusing the term. Its use requires the dog to first be capable of thought. Metacognition is basically the ability to analyze your pre-existing thought processes. A dog's ability to be trained does not suggest the dog is "thinking."
So, let's try another tact. How would your questions be answered if dogs could think? If they were self-aware? If they could complain about their work environment?
(1) Of course a dog would be capable of training another dog. Probably quite a bit faster. While there are arguments about how predictable my next insight is, there are too many people who observe it to dismiss it: later children tend to learn things faster than earlier children because the earlier children act as a more relatable bridge than adults.
However, this presumes cognition means the ability to speak or otherwise communicate. Dogs don't have the vocal structure necessary to create complex sounds. Could they develop a barking/whining language? Yes, perhaps, but we're beginning to stretch credibility. Harlan Ellison's A Boy and His Dog solved this problem with telepathy.
(2) Subservient? Not necessarily. Dependent? Completely. In a Utopia intelligent man and intelligent dog would live in a happy world of symbiosis. But, humans can't help making slaves (even in the U.S., even today) of one another, so a Planet of the Apes scenario is much more likely.
(3) We do not know why the bond between humans and dogs is so strong. It's unlikely that it would vanish with the onset of intelligence just as the bond between humans has not devolved with the onset of our intelligence. However, with the ability to think, dogs would have the ability to overcome the desire for that bond when it is not valuable to them — kindof. Domestic Violence suggests that intellect alone is not enough to break bonds in all cases. So, generally, yes, they'd still desire to please us (see Planet of the Apes, above).
(4) I'm willing to go out on a limb and suggest that the days of Human A visiting Human B to stud their puppy would end — well, at least without one or both of the dogs getting their piece of the pie. The body of legal precedent that would be built around pimping dogs would become very large, very quickly. It makes one wonder if the first canine judge would have the temerity to tell the first slob human before his/her bench to "Sit!" (Activists would likely call the moment wholly justified because of the thousands of years of specieism that dogs had to endure. The canine judge would probably shake his mane and say, "what? I hear humans tell defendants to 'Sit!' all the time!")
Note, however, that wolves are generally thought to mate for life. Note that it's generally the alpha male and alpha female that mate for life, and the connotation has nothing at all to do with what it means for humans to be monogomous because dogs don't think about it, they react to it. Alpha female wouldn't reject alpha male because he's ugly — but a human female will reject a human male because he's ugly (unless he's rich enough... Ah, intelligence!) So, yes, it might lead to mating for life, especially after the first canine alimony case.
(5) I've seen birds, cats, and dogs raised together such that they wouldn't hurt one another ever. I've seen dogs rip cats apart and cats eat birds. If we grew up together, it would substantially increase the liklihood of a utopic symbiotic relationship. If it happened right now, it would take the passage of human generations to get even the majority of humans to see dogs as equals (look at how long it took for the majority to be sympathetic enough toward homosexuality just to grant them the right to marry).