Determining the paleoelevation of mountain ranges
I'll begin with your second question, as to how mountains erode.
To simplify things, there are two methods:


Physical weathering, where the rocks are broken down by weather. For example, there are cracks in rocks that get filled by water which freezes and expands. This maker the cracks bigger and breaks down the rock. Also wind, earthquakes and any other process that breaks it down.
Chemical weathering, where the rocks are not broken by are altered to softer and weaker types of "rock". For example, take granite, a common rock in mountain ranges. It contains minerals from the feldspar family which are solid and hard. However, give some time and water and they convert to minerals from the clay family (aka "dust").


The first process is more relevant for tall mountains.

Now, how do we know the rate? This is a competition between uplift (the rising of the mountains) and the weathering (the breaking down of mountains). I'll give one example to illustrate it. Let's say that on the mountain top you find limestone with a certain fossil that you know existed 5 million years ago. So you know this used to be at the sea floor, let's say 300 meters below the water, but now it's 2000 meters up in the sky. So it had to rise 2300 meters in 5 million years. You can calculate the average uplift rate from that. Also, let's say that you know that in the past 10 years, a certain amount of rock was eroded from the mountain. You can calculate the rate of weathering. This way you can know the total rate.

There are new modern methods which rely on cosmogenic isotopes to get a much more accurate picture of this process, but that's for another question.