Adapter load switch MOSFET schematic questions
1) R12 and R13 limit the inrush when the adapter is reversed.  In that case, V_IN is negative with respect to ground.  Q7 turns ON, shorting G-S of Q1 and Q2, ensuring they're OFF.  Alas, the "body diode" of Q1 is now ON, connecting the (negative) V_IN to the IC ACDRV and/or CMSRC pins -- in basically current-unlimited negative polarity (with respect to ground).  So, if e.g. ACDRV had a safety diode that normally would shunt more-negative-than-ground -- now that (tiny) diode is 100% forward biased with ump-teen volts across it and nothing to really dampen that current.  "So, the smoke will escape" and we all know what that means :)  Hence the need for R12/R13.

For 2) I can't imagine.  The datasheet goes into a lot about "voltage spikes when the adapter is plugged in" although I can't see why C1 would make any difference.  It's not mentioned in the datasheet.

For 3) Again I can't imagine.  This is a MOSFET gate with megohms or gigohms of input Z.  Yes, considerable capacitance, but 4.7Ω?  Why not the same for the other MOSFET?  Crazy stuff.

Hope this "1/3 of an answer" helps.