Hello lifewouthumans
Here's the official datasheet for this NP. I don't know if this is the one you were using.

In response to your questions:
0.- Yes, that is the correct PIN distribution
1.- The voltage difference between +Vout and -Vout will range from approximately -1 mV to +41 mV, depending on the pressure applied (0 to 200 kPa)
2.- Likewise, you would have a maximum value of up to 41mV, but I personally recommend that you always measure +Vout and -Vout, considering that this way you will have greater precision.
3.- No, as long as it is not exposed to temperatures and pressures outside those recommended, recalibration is not necessary.
I hope this information has helped you, please let me know if you need help with anything else.
Have a great day and best of luck.