How are determined experimentally the energy levels of the atoms ? How is the calibration done to several decimal points? I see discrepancy for the absorption edges for the atoms in the X-ray ?
For example K-absorption edge of carbon can be anywhere between 282 to 284eV according to different sources. 
My question is how is energy measured and calibrated ?
Are the energy levels determined by electron collisions with specific eV ? 
 A: It is possible to measure wavelengths of light to many decimal places.  When you see accurate determinations of atomic energy levels, they were done spectroscopically, looking at absorption or, more commonly, atomic fluorescence.  Since $E=hc/\lambda$, one can accurately convert between wavelength and energy.
When excited, atoms emit many wavelengths of light.  By examining patterns in these wavelengths, one attempts to assign them to transitions between particular atomic energy levels.  As an example, one can look for wavelengths that fit the pattern of a rydberg series, that is of transitions to some particular lower level from a series of highly-excited upper levels.   Because highly-excited levels are hydrogen-like and therefore well-understood, one can immediately deduce the energy of lower level from from the observed wavelengths.       For much more information on this process, see the NBS monograph entitled Atomic Energy Levels As Derived From the Analyses of Optical Spectra by Charlotte Moore (NBS Circular 467).
As an example of accurate wavelength measurements, you can read here about a commercial instrument which measures wavelengths accurate to 1 pm or better (1pm=$10^{-12}m$).
Beams of electrons cannot be created with anything like that level of precision.  Consequently, electron-atom collisions are rarely, if ever, used for atomic energy level determination.
A: Soft x-ray optics typically uses grazing reflections on suitable mirror materials  and gratings (e.g. Pt coated optics) or crystals and the detection can be done with scintillators using CCDs or PMTs. Commercially available instruments have approx. 0.2eV resolution (2000 lines) while research grade instruments can achieve much higher resolutions e.g. 30000 lines for this instrument (albeit a slightly higher energy): "Very high resolution soft x-ray spectrometer for an electron beam ion trap" P. Beiersdorfer et al. in Reviews of modern instruments. 
