2060 (10%), 2110 (50%), 2210 (90%).

It depends on what you mean by "badly done". If it's "good, but not good enough", 99%. (It's possible for an AI that hasn't been carefully designed for invariant-preserving self-modification to nevertheless choose an invariant that we'd consider nice. It's just not very likely.)

Hours: vanishingly small. Days: 5%. Less than 5 years: 90%. (I believe that the bottleneck would be constructing better hardware. You could always try to eat the Internet, but it wouldn't be very tasty.)

More.

Yes - mostly because true existential risks are few and far between. There are only a few good ways to thoroughly smash civilization (e.g. global thermonuclear war, doomsday asteroids which we'll see coming).

No. This is essentially asking for a very hard problem that almost, but not quite, requires the full capability of human intelligence to solve. I suspect that, like chess and Jeopardy and Go, every individual very hard problem can be attacked with a special-case solution that doesn't resemble human intelligence. (Even things like automated novel writing/movie production/game development. Something like perfect machine translation is trivial in comparison.) And of course, the hardest problem we know of - interacting with real humans for an unbounded length of time - is just the Turing test.