But not even a super-intelligence can find ways to self-improve that don't exist. We don't know what we don't know and we don't know if it's possible for intelligence to improve indefinitely. If there is a hard limit to the amount of improvement an intelligence can acquire, then superintelligence is not going to happen.
As an analogy, think of the speed of light. No amount of technology will get you past that. You might find a way around it for the purposes of interestellar travel but nothing will ever move faster than light.
How can we know that there don't exist similar impassable barriers for the development of intelligence? Maybe it is an -yet undiscoered- law of intelligence that an intelligent species cannot create an artificial intelligence more intelligent than itself. Who knows?
The problem is that we can sit around thinking of possibilities and impossibilities for ever, but the fact of the matter is that we don't, currently, have any evidence to the point that super-intelligence is possible. We don't have any evidence to the contrary either- but the discussions of superintelligence start with people assuming it is possible and that is an assumption that must first be substantiated (but rarely is).
Yes, exactly. General intelligence is "thinking about thinking", and that inevitably entails removing bottlenecks in creative ways.
The whole reason that some people predict an intelligence explosion is because intelligence is the resource that can find arbitrary ways to self-improve, other than tuning one specific parameter.
I would go so far as to say that intelligence is the same thing as the ability to make improvements that climb out of a local domain of attraction.