Best way to Step down 6V DC or 9V DC for 3.3V DC operation
The FET is for reverse polarity protection. This could be an issue because CR2032 cells can easily be installed backwards in some holders.

TPS62745 doesn't need an external flyback diode because it has an internal FET to perform this job. The technique is commonly called 'synchronous rectification', because the FET operates like a diode which is switched on and off in synchronism with the PWM. The FET also has a 'body' diode across it which does the job during switching before the FET turns on.

Possibly, depending on size of a Tantalum vs a ceramic capacitor with the required capacitance at the working voltage. Small high value ceramics often have reduced capacitance at higher voltage. however ceramic capacitors usually have lower ESR which reduces ripple. If you need much higher capacitance a combination of types might be best.