Resistors on decoupling capacitors in ADC Layout Guidelines
What is the purpose of the resistors in series with the
ground-decoupling capacitors for the REFCAP and REFIO pins (4 and 6)?

The datasheet says the REFCAP is a &quot;ADC reference buffer decoupling capacitor pin&quot;, I believe this is to force the REFCAP's capacitor ground to be refered back to the ground of the ADC (rather than some other point on the board) to reduce noise. A small voltage difference could exist on the PCB if the grounds of the caps were placed elsewhere and lead to error.

What is the purpose of the series resistors immediately after the
capacitor on the analog input pins (the two directly below 5 and 6)?
What about the next resistor immediately in series on the analog
ground trace (why is it it not pointless)?

Forms a differential input filter with the capacitor tied to pins 5 and 6. The second resistor in series is most likely to make minor adjustments with two resistors (ie 100 and 1 ohm resistors or 100 and 5 to make a total of 105 ohms, (not actual values just an example)).
Finally, if it isn't obvious from your explanations, what are reasonable choices for these resistances? (If input signal frequency really matters, please assume ~50Hz.)

What is the purpose of the parallel resistors in the optional &quot;Analog
Input&quot; section (does this have something to do with current-limiting
the TVS diode?)---presumably something to do with the inductance of a
big resistor?

Again it's for tuning or using one or the other if you want to test one size of resistor vs the other size.

Finally, if it isn't obvious from your explanations, what are
reasonable choices for these resistances? (If input signal frequency
really matters, please assume ~50Hz.)

The resistors make and RC filter, the filter pole is the bandwidth of your analog input. For example: If your application needed DC to 1kHz then set the RC pole to 1kHz.
Here is more information on RC common mode filters and how to set them