To me I don't really care, I go with the defaults. I find it convenient to use as a mesh check though. Make a plot that's nodal, then an identical plot but on elemental. The differences in the distribution and values should be relatively small, if the differences are large it can indicate your mesh is inadequate for your problem and you should consider making the mesh finer.
Nope, sorry, just that... well the averaging is different. When you work with FEA you'll always have some kind of averaging because it's an approximate result. Don't know the background beyond that article but it just works
mesh check through, or mesh convergance is simply a plot of the rate of change of a parameter such as stress, strain or displacent with repect to a mesh larameter such as total number of nodes or elements. it shows how changing the mesh resolution impacts on the result. when there is little change in stress for example even when the mesh element size is reduced further you can assume your element size, or number or nodes is adaquate or converged. a simple way to do this is to record the number of elements and the max stress, then make the mesh finer and record the max stress and number of elenents. repeat this process at least 3 times and plot on a graph. when you see that by increasing the number of elements has little or no effect on max stress you know ypur mesh is good. an. important point to note is that if you have sharp corners on your geometry your mesh will never converge, this is call mesh singularity, and is in brief terms caused by the software trying to calculate stress for an infinately small area.
Element stresses are just that, stresses calculated for the element at the gauss points typically. These stresses are extrapolated out to the nodes and then averaged to give nodal stresses. This has to be done because strain is not continuous across element boundaries, just displacement is continuous. Sooo...if your mesh is such that the extrapolated nodal stresses for each element differ by a great deal then you have an indication of the need to refine your mesh.