Hi,
1) "I" stands for current."OUT" for the pin/signal.
(the abbreviation for the BAT signal should be I_BAT)
2) the state column shows: "IN" powered as well as "BAT" powered, referring to the "IN" pin and the "BAT" pin respectively.
3) did you read the documents the manufacturer provides on the device´s internet site? (like AN1260)
Basically the VRef, Thermal block, Charger, syncDiode .. are just shut down when not needed to save power.
This is what the table says ..
Klaus