Dammmmmmmn those be good questions!! That's awesome!!

The easiest way to measure the thickness of layers in the earth is by using Seismic waves -- these are sound waves that travel through the earth. We use huge sounds at the surface of the earth (sometimes dynamite for shallow layer mapping, or you can use the sounds made by big earthquakes to measure the layers through the whole earth) and you track how long it takes for the sound waves from the explosion to go through the earth. The seismic waves will bounce back at composition changes (where you have a change into a different rock unit).

The speed of the seismic waves will change depending on which rock layer it's traveling through (the properties of each rock layer change how fast sound travels in it). We can then calculate how long the sound takes to travel through each layer, and from that we calculate the thickness of each layer. The amount of time also tell us about the properties of each layer, and this exact method is how we found out that the outer core is liquid, but the inner core is solid!

As for the temperature inside the earth, we calculate the innermost temperatures of the earth from what we know about its composition. The inner core is solid while the outer core is liquid, but they have pretty much the same composition -- mostly iron. In the lab, we can simulate the pressures inside the earth, and see how hot we have to make it for solid iron to melt. That should be the temperature at the boundary between the outer core and the inner core.

As for the rest of the earth, mostly we make a gradient from the temperature at the surface of the earth, and it gets increasingly hotter as we approach the core. We call this the geothermal gradient and other than in places that are oddly hot -- usually near volcanoes and such-- this gradient does a pretty good job of estimating temperature with depth in the earth.

Please look at the picture on the following link:
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