I don't think that's right.
An object on the surface of the earth has a "sideways" velocity relative to a fixed frame of reference of slightly in excess of 1000 mph.
When it gets to the top of the 100,000 km ribbon, on its way to Mars for example, it's got a speed relative to that same fixed frame of reference of roughly 17,000 mph.
Where'd that other 16,000 mph come from?
Using a conventionally-launched orbiter, the launch rocket climbs vertically for a short period of time, but quickly rotates off the vertical to start developing the 18,000 mph necessary for low-earth orbit.
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.
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.