1 why forest
Neutral hydrogen atoms in their lowest state will interact with whatever light has been redshifted to a wavelength of 1216 angstroms when it reaches them. The rest of the light will keep travelling to us.
2 why absorption lines
if you shine a light with wavelength 1216 at a bunch of neutral hydrogen atoms in their ground state, the atoms will absorb the light, using it to boost the electron to a higher energy state. If there are a lot of neutral hydrogen atoms in their ground state, they will absorb more and more of the light. So if you look at the light you receive, intensity as a function of wavelength, you will see a dip in the intensity at 1216 angstroms, depending on the amount of neutral hydrogen present in its ground state. The amount of light absorbed (‘optical depth’) is proportional to the probability that the hydrogen will absorb the photon (cross section) times the number of hydrogen atoms along its path.