Could this crack in shower caulking be causing drywall damage to the subfloor?
Could the crack cause damage below on a lower floor? 

Absolutely most tile is inside the pan but the backer whatever was used is outside so if the water gets past the grout it can run down. 
I would say that little bubble looks like a bad tape job because there are no watermarks I can see. As far as that is concerned I would use a t pin or hat pin and pole a tiny hole there just to make sure, if the spot was caused by water it may drip and that tiny pin hole can help it to dry out. As far as the hole next to a penetration we go for the best utilization of the Sheetrock the hole could be between 2 sheets as any pro will tell you.  

The crack can be caused by the corner not being tied when I plan on installing tile I lock the corners (framing together so they will not flex and crack. If not tied calking is better than grout

Last I have pulled dozens of shower and tub shower surrounds that had no barrier. I have found some builders that glued the tile directly to water resistant Sheetrock, I have also seen many with backer board and nothing else.
 It is possible the crack originally was just calking I know contractors that regularly do this to try and prevent corner cracks. Clean it out the best you can and fill with calking, make sure to use a kitchen &amp; bath type these have mold inhibitors.
Good luck.