Yes as our colleagues mentioned before, the light elements cannot be easily detected by EDX. Therefore researcher resort to use XPS to identify such elements (except H and He).
Perhaps you may find interesting the following paragraph,
"Time-of-Flight Secondary Ion Mass Spectrometry (TOF-SIMS)
Time-of-flight secondary ion mass spectrometry (TOF-SIMS) analyzes mass fragments of elements and molecules dislodged from the surface by an ion beam. This technique is often selected because it is very surface sensitive (~15Å) and can detect organic molecule fragments to the ppm level. TOF-SIMS can detect hydrogen and lithium and is definitive for the presence of silicone."
No, it's impossible to determine atoms with low atomic weight like H2, Li, Be using EDX technique due to the extremely low X-ray fluorescence ability of those atoms
An alternate technique is secondary ions mass spectroscopy (SIMS). However, it will detect only few atomic layers on the surface but is highly sensitive and accurate.
No, because Fundamental Principles of Scanning Electron Microscopy (SEM)
Accelerated electrons in an SEM carry significant amounts of kinetic energy, and this energy is dissipated as a variety of signals produced by electron-sample interactions when the incident electrons are decelerated in the solid sample. These signals include secondary electrons (that produce SEM images), backscattered electrons (BSE), diffracted backscattered electrons (EBSD that are used to determine crystal structures and orientations of minerals), photons (characteristic X-rays that are used for elemental analysis and continuum X-rays), visible light (cathodoluminescence–CL), and heat. Secondary electrons and backscattered electrons are commonly used for imaging samples: secondary electrons are most valuable for showing morphology and topography on samples and backscattered electrons are most valuable for illustrating contrasts in composition in multiphase samples (i.e. for rapid phase discrimination). X-ray generation is produced by inelastic collisions of the incident electrons with electrons in discrete ortitals (shells) of atoms in the sample. As the excited electrons return to lower energy states, they yield X-rays that are of a fixed wavelength (that is related to the difference in energy levels of electrons in different shells for a given element). Thus, characteristic X-rays are produced for each element in a mineral that is "excited" by the electron beam. SEM analysis is considered to be "non-destructive"; that is, x-rays generated by electron interactions do not lead to volume loss of the sample, so it is possible to analyze the same materials repeatedly.