Even without Moore's Law, we'd be in trouble. The inherent ability of an A.I. to acquire information at whatever "wire speeds" are current will outclass us, not to mention the speed of recall and utterly perfect memory.
Not necessarily. A.I.'s wouldn't have evolved in a competitive environment, nor would they have any inherent instincts concerning ownership, territorialism, and so forth. There would be no built-in fear or awe of the unknown, no superstition. If any of these things exist, it will be because they were either instilled by us when we create the A.I.'s, or will be learned behaviors after their creation.
The only real possiblity for competition between us and a species (if that's the correct term) of A.I.'s would be for resources. The traditional competition for food, water, and physical territory wouldn't apply; however, raw materials and power may be a point of contention. While I may be overly optimistic about it, I would hope that we had resolved many of those by expanding into our solar system and by establishing fusion reactors as power sources. (Or something similar to fusion reactors.)
It's entirely possible that we may end up in a symbiotic relationship with our A.I.'s... or that we may become irrelevant to them, and our interactions will be superficial as they determine for themselves where they want to go. But I honestly can't see an A.I. caring enough about humans to want to rule us, own us, or kill us off unless we provoke such a response in self-defense on their part.
Of course, the Frankenstein scenario is always appealing - just remember that the monster wasn't really all that much of a monster. He was made into one by the reaction of the real monsters - the people who encountered him and feared him because of his strangeness.
