Yes, but as altitude increases, orbital period decreases; in other words, the farther “out” an orbit is, the slower its motion relative to the Earth’s surface. At an altitude of approximately 35,786 km (22,240 statute miles), the orbital period of the space elevator’s center of mass is equal to the Earth’s period of rotation, 23.934 hours. The elevator is moving “sideways” at the same speed the Earth’s surface is moving “sideways”, and so the elevator appears to hover over a point on the Earth’s surface.
Not true.
The angular velocity is the same; 360 degrees per 24 hours, but in 24 hours an object on the surface of the earth moves 25,000 miles (the earth's circumference), but an object in geostationary orbit moves over 150,000 miles.