Extreme cold can happen in climate change.
Definitely not. The fastest warming portion of the planet is the Arctic and that's where the extreme cold has to come from. There are indeed fewer record lows over time, although Michigan and Illinois (I think) both set all-time state-wide record lows for the month of April. But if this cold pattern had happened 30 or 40 years ago, there would have been more record lows.
Yes, that's been known to happen...
I grew up in the Finger Lakes region of New York. We were under a mile of ice only 15,000 years ago which isn't that long ago when you think about it.