Frequency band mofications for Samsung Galaxy S4
Ok then, let me begin by answering in order


This is possible if the previous owner flashed their own hybrid modem onto their phone, which allows phones that are physically able to use a  certain band (1700/2100) in your case, but the company does not allow it on their stock modem (for many different reasons). The hybrid modem basically overwrites the old modem that in short, says to the phone, "Hey, these are the only bands you can use", while a hybrid modem tells the phone, "Go crazy", and unlocks all or certain bands at a cost of battery life (more bands, more battery is needed to power it.)
Most probably, yes.  A factory will wipe out the hybrid modem and replace it with the stock. So only update if you have a copy of the hybrid modem, and know how to flash it. (ODIN)


I hope this answers it for you.