Trying to understand behavior of p-FET in lipo charger circuit
Some answers:

1) Sounds good to me :-)

2) This is less complex than you think, since Vg is 0 the PMOS will just conduct. The Drain-Source diode does not come into play as the PMOS will simply short it (as you noted). Note that when a MOS transistors is on it will conduct a current from Source to Drain but also from Drain to Source. It is basically a symmetric device (disregarding the diode for a moment).

3) No the diode in the PMOS is shorted, the PMOS will conduct the current. The only difference between figure 7 and directly powering from the battery is indeed only the Rds_on of the PMOS. Which is low, so you probably would not notice the difference.

4) This looks like a fine choice to me, an alternative could be the SI2301 which is cheap but also very small (SMD type housing).