Your third point is valid, but your first is basically wrong; our environments occupy a small and extremely regular subset of the possibility space, so that success on a certain few tasks seems to correlate extremely well with predicted success across plausible future domains. Measuring success on these tasks is something AIs can easily do; EURISKO accomplished it in fits and starts. More generally, intelligence isn't magical: if there's any way we can tell whether a change in an AGI represents a bug or an improvement, then there's an algorithm that an AI can run to do the same.

As for the second problem, one idea that may not have occurred to you is that an AI could write a future version of itself, bug-check and test out various subsystems and perhaps even the entire thing on a virtual machine first, and then shut itself down and start up the successor. If there's a way for Lenat to see that EURISKO isn't working properly and then fix it, then there's a way for AI (version N) to see that AI (version N+1) isn't working properly and fix it before making the change-over.