1. If I power the PF8200 locally as I described, should I still be able to use the KITPF8200FRDMPGM programming interface?
Yes , I recommend you read the script which use to burn the OTP , the operation is so easy, TBBEN is high ,PWRON is low , and then provide a 8V(you can even supply externally), then write the mirror register. TBBEN Low and VDDOTP low.
2. From the datasheet, I see that VIN has certain rise time requirements (VIN must reach UVDET in 10 to 1500us). Does VDDIO have any similar requirements?
No,even for Vin ,there is also no requirement as you said, this is just tell customer the process for 5ms power up. so VDDIO and VIN ,just all keep on when you burn the OTP.
3. Does it matter whether VIN or VDDIO is applied first?
No,but i recommand VIn in front of VDDIO.
I upload a PPT in this link and you can also just use KL25Z to burn OTP on your board.
https://community.nxp.com/docs/DOC-344151
PMIC and SBC question