Hive's freedom of movement rule - can you 'pass over' a gap that you can't go into?
Yes,

the ant can move to all spaces marked in yellow. The only restrictions to movement are that it must remain attached to the hive and you can't move into spaces you cannot slide into. 

It can cross these "caves" because it continues to be touching the hive when it moves, and that continual touching to the hive (and the sliding rule) are the only requirements.

When moving any piece (but the hopper and when jumping the beetle up onto the hive), it must always remain in contact with at least one tile during the entire movement from beginning to end.