1. It allows a trickle charge current through to the battery even when the regulator has shut down. It also makes it think the battery is fully charged if it is disconnected so the regulator automatically shuts off when no battery is present.
2. It allows the IC to 'sink' but not 'source', it can drop the voltage at that point by making it's output pin go to low voltage but if it goes high, it can't force current into the circuit.
3. To deliberately give the LM301 a poor high frequency response, making it reactive to slow voltage changes but not noise or interference.
4. It doesn't monitor voltage at all but it does monitor current. The LM301 changes output state when the voltage across it's inputs reverses polarity. The voltage at the + input is held at 1.165V by R2 and R3 (note the voltage across the ground and output of the LM338 is fixed at 1.24V). The voltage at the - input comes from after the 0.2 Ohm resistor. When the voltage across the 0.2 Ohm resistor exceeds 1.165V the LM301 changes output state and cuts the charging current. It follows that the current limit is approximately 1.165/0.2 = 5.8 Amps.
Brian.