Source on that last one? Even the worst climate change predictions don't create an earth unsuitable to human life. Hostile changes, sure. Unsuitable? No.
That would only be in the worst case scenarios, and even then only a transitory condition. You can't keep humans down forever, sooner or later we'd rise again. It's debatable what it would take for civilization to collapse, and how long it would take to recover. But I think there's little doubt that recover it would.