How far above the Earth does Earth's atmosphere end and space begin?
The atmosphere end where the atmosphere pressure is zero. Pressure is linked to temperature therefore the atmosphere does not have a well-defined end. It can vary
At the Karman line.
There are a few possible definitions for the end of the atmosphere and beginning of space. International convention however accepts that at the Karman line (100 km) the atmosphere ends and space begins. At this point the atmosphere is too thin to contribute to lift of a plane or shuttle. It is also the point where the atmosphere is no longer of uniform composition.
However, arguments can be made that the top of the atmosphere is 10,000 km where it merges with the solar wind and also 1,000 km which is the base of the exosphere.