Crystal Field Explanation of Colors of Coordination Compounds
Your assumption that the electron emits a photon when transitioning back to the ground state is not entirely correct.

The excited electron can also transition back by transferring the excitation energy to heat energy. The compound then warms up ever so slightly and the electron is buzzing away happily in the lower $d$ orbitals.

As to your P.S.-ed question, I'll quote Wikipedia:


  The main factors that cause broadening of the spectral line into an absorption band of a molecular solid are the distributions of vibrational and rotational energies of the molecules in the sample (and also those of their excited states). [...] In gas phase spectroscopy, the fine structure afforded by these factors can be discerned, but in solution-state spectroscopy, the differences in molecular micro environments further broaden the structure to give smooth bands.