They have to be removed. The O2 sensors will continue sending information to the ECU about stoichiometric air/fuel values. This information will constituent adjusting the mix based on stock recommendations. Removing the sensors lets the flash tune set the fuel mix.
Oh crap I didn't cover the pins or moisture-proof my ECU before mailing it off. Should be fine though right?
Probably not an issue unless UPS gets it wet. I got mine back from 2WDW without any specific protection. The box itself was very secure and packed well, but the connectors weren't covered. Probably not a big issue. I just like to be cautious.