There's nothing in principle that prevents machines from learning methods. For example, there's software that can learn some simple algorithms: http://arxiv.org/abs/1410.5401
> Do we know what intelligence is?
It's hard to pin down exactly what anything is (unless it's something we constructed from axioms). I'd be hard pressed to tell you exactly what a car is (must it have exactly 4 wheels?) -- but I still look for them when I cross the street.
You know intelligence when you see it. Bill Gates is more intelligent than a fish. That's a useful distinction to make in the world! (And that's what words are for)
> Why would be make something to imitate our own?
It's economically valuable! That's why Facebook, Google, Microsoft, Baidu, IBM are collectively investing billions of dollars per year.
> Would an artificial system have curiosity? (perish all the Internet cats!)
From the outside, curiosity looks like a drive to explore without a definite prediction about how it might help you achieve ultimate goals.
Curiosity in that sense should automatically appear in some (theoretical) systems -- for example, Marcus Hutter's AIXI formalism (https://en.wikipedia.org/wiki/AIXI).
More concretely (but less directly akin to curiosity), algorithms that make tradeoffs between exploitation and exploration, such as solutions to the Multi-armed bandit problem (https://en.wikipedia.org/wiki/Multi-armed_bandit) could display a kind of curiosity. When faced with a number of lotto levers, with independent and unknown payout schedules, the optimal solution involves switching around between exploiting known high-payout levers and becoming "curious" and trying out new levers.
The Monte Carlo tree search (https://en.wikipedia.org/wiki/Monte_Carlo_tree_search) algorithm used to make Go AIs employs such a strategy (http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.102....). The algorithm tries out certain variations of play, and then sometimes becomes "curious" as to whether certain other lines of play might be better, and switches over to deepening its investigation of them.
These are just examples of things that are somewhat functionally equivalent to curiosity from the outside -- it says nothing about the internal sensation of curiosity that humans experience. I have no idea what's necessary for that!
> Why do we think that intelligence would escape and kill us?
If there _were_ extremely intelligent software (a huge if!), it does seem ridiculous to claim that it'd escape or hurt people. Why would it be driven to do such a thing? The argument espoused by some very smart people e.g. Elon Musk, Stuart Russell (http://edge.org/conversation/the-myth-of-ai#26015), Bill Gates, Stephen Hawking, et al runs a bit like this:
Intelligent software, without being malevolent per-se, might in the pursuit of its goals incidentally do things that people don't like. (More on this line of reasoning: https://selfawaresystems.files.wordpress.com/2008/01/ai_driv...)
Humans don't harbor a particular ill-will towards ants, but if we become interested in some (orthogonal) goal like building a basement for a house, we might along the way destroy some ant colonies. When human-level intelligence arrived and went about its business, it led to the extinction of quite a few species.