Which crystals can a Geologist collect?
Frederic Moyersoen, the designer of the game, clarified it should be option 1 on BGG here (emphasis mine). 


  Consider the geologist as someone who picks up the crystals as they are discovered. As the crystals are printed on the cards and cannot be physically be picked up, we just count the points at the end of the round. We don't care if a path connects to the crystals or gold.