Clarification on absorption spectra and crystal field theory
You would expect a sharp peak for a well-defined structure which has bond lengths and angles that do not significantly change. In a crystal structure at low temperatures you may be able to observe sharp peaks rather than broad bands.

In solution, however, there is a number of effects that broaden the peaks, making the entire thing less sharp:


aqua ligands can dissociate and reassociate; if the photon hits the complex while the structure is different, the wavelength will be, too
typically, the ligands of a complex vibrate both symmetrically and antisymmetrically. Both vibrations lead to structure changes, therefore electronic changes and thus changes in the absorption wavelength.


Different solvents will give different peak broadening (I saw a graph once, but I can’t remember where it was).

The titanium(III) spectrum is also more complex, by the way. If you look closely, you can see a shoulder on the low-energy side of the main peak. This is because the excited state is Jahn-Teller distorted, and there is not one but two transitions possible that slightly differ in energy. (The ground state is very, very weakly Jahn-Teller distorted, because there is not much energy to be gained.)



After a molecule has absorbed the energy of a photon and went into an excited state, there is not only the simple rerelaxation that would emit a photon of the same wavelength to return to the ground state. Rather, by a set of complicated mechanisms, the energy can be transformed into vibration (more and more vivid than before) and thus slowly released in form of heat. That is why a solution that absorbs light will warm slightly.