In answer to your first question no there isn’t a document with this written down (unless you count the code)

upts are solution points
qpts are quadrature points
fpts are flux poitns
spts are shape points

Prefixing with a n tells you the number of those points. fpts are the flux point weights. I don’t recognise npts_coeffs but that is probably because it is an abstracted name that is used in some function. Same with npts_cdenom. (Although I would guess that cdenom i sthe the demoniator of whatever npts_coeffs).

Freddie’s paper on finding quadratures is a good place to start (Redirecting). The polynomal basis depends on the eleement type but Hesthaven and Warburton 2008 is a good book for these. Generally for some chpoice of polynomial degrees we evaluate some combination of Jacobi polynomials at the solution points to form a Vandermonde matrix. shape.py is a good place to start as is solver/base/elements.py