Home engineering = cool, real world applications, RUN from this. First and foremost, no gloves?
Next, 808nm is not the proper wavelength, every commercial machine runs at 1064, and 2 others for harder colors, but 95% of tattoos can be removed at that wavelength. There is no talk of pulse control either and his depth gauge is a guess, at best.
Further signs that the guy, while apparently smart enough to rig this up, does not fully understand what he's doing - he states in the first video "dude, I can see the ink changing colors" - which is false. The white you see is actually water vapor, from the laser exploding it within your skin. Lasers do not remove tattoos, they facilitate the body to dispose of the pigments.
You wouldn't go to a kitchen magician for a tattoo, why go to one to have it removed?