1. It is meaningless to say "spin at 28,437 km", as rotation needs to be measured as angular velocity. (deg/hr, rad/sec. etc.)
I know that it is common to express this in terms of tangential speed( in this case, at the equator) But it is sloppy and can lead to misunderstanding. For example if the Earth had a tangential speed of 28,437 kph at the equator, then at 45 north latitude it would only be 20,105 kph
As swansont has pointed out there is a speed where the centripetal force (the force required to keep an object moving in circle) and the gravitational force balance out. This would result in the object going into orbit around the Earth. Gravity is still in play. In fact it is gravity that would prevent someone standing on the equator from just shooting out into space at in a straight line instead of just hovering over the Earth. And by the way, your number is a bit low, the equatorial speed would need to be 28463 kph
And because of what I alluded to earlier, only someone on the equator would even go into orbit. People elsewhere will feel lighter, and the ground would seem to tilt a bit under their feet ( And even this is an over simplification which assumes the Earth maintains its present shape. If the Earth was indeed spinning this fast, its very shape would change, making it much more of an oblate spheroid.