Does the gap created by a rock-fall have to be replaced to make a continuous path before additional cards can be added on to the disconnected portion of a path? Or can you continue to extend the disconnected path in the hopes of filling in the missing link on a later turn or allowing one of your teammates to potentially fill in the gap?
All new tunnels must connect to the ladder. This was answered by the Designer on Boardgamegeek.
when you play a path card it must be able to trace a path back to the start card.
See Pat Ludwig's answer - you can't play cards on a disconnected path.
However, my group has always played that you can still continue the "disconnected" portion of the tunnel. Of course, you can't win until it's reconnected to the start.
We've always justified this by explaining that some dwarves were trapped in the disconnected portion of the tunnel after the fall :)