Absorption and emission at same wavelength?
Yes it is very common particularly in the more rigid type of molecule. The best example is chlorophyll and this overlap of absorption and emission leads to energy transfer in photosynthesis.  The reason for the overlap is that the excited state potential energy profile is very similar in shape but slightly shifted (as displacement) to that of the ground state and this results in a 'mirror image' spectrum. The spectra below are from anthracene.


You can see even in this rather crude figure that there can be absorption and emission at the same wavelength.