caves

The cave rules, arranged by sequence of play.

I wish to confirm that I understand the Cave LOS rules correctly. The first image shows the map area without the Cave counters. The second image shows the map with two Cave counters. It also has two "LOS threads". I believe that the red one is blocked and the gray one is clear. What do you think?

"The Americans win at the end of any CG Assault Period (...) by Controlling all land (including undestroyed pier) hexes of Gavutu and Tanambogo..." I think that a Japanese unit sitting in a cave doesn't control a land hex. Is this the case?