I agree with @Samuel's suggestion that a few of these questions are better served else where. point up to you bud!
On that note your second question might have more to do with where Man is technologically when this hypothetical scenario occurs in the World you are building. Are we in pre-bronze age? current modern technology? or distant future where we have already traversed the stars and are spreading through the galaxy like a new plague? :) Will we survive or go extinct? So many factors here to consider.
As for the numbers, you can use these to get you started on your World Building project. The Earths current rotation is moving at 1675 km/h or 465 meters/second. The equator is 40,075 km and the length of time the Earth takes to complete one full turn on its axis is 23.93 hours for a sidereal day.
40,075 km/23.93 hours = 1,675 km/hour
As for the Cores rotation, yes you are correct they turn at different rates, and from what we currently know they actually move in Opposite Directions (this could be a great point for creating an inner world within your outer world for a game). It is understood from most studies that Earth's inner core is rotating faster than its surface by about 0.320 - 0.516 degrees per year.
As for changes (another great anomaly that could effect the world you build if they were over emphasized) researchers speculated that if the Earth's inner core is rotating faster than the rest of the planet, then shock waves from waveform doublets would enter and exit through different parts of the core despite originating from roughly the same spot on the planet's surface.
Another fascinating point recently being discussed in Scinetific communities is that the Daming of river systems around the globe is causing the earths roatation to slow down. You can read more here
So I hope those numbers help you in your World Building project.