Pico's Mosfet maximum Amperage when partial ly turned on?

Hi,

I'll answer below, but I think the real answer is:

The FET is connected to the VCC/VBAT voltage rail, and you can't use it like a voltage regulator - so unless the GPS has its own voltage regulator, using the FET won't be a viable option for you. You'd be better off adding your own to the 3.3v rail.

a-Does that mean that I will get a 3.3V on VBAT?

No, with nothing connected you'll get VCC/VBAT's voltage on BAT_IN.

b-What would be the max amperage in this case?

It totally depends - basically it turns the FET into a resistor. With that little drive voltage the datasheet doesn't specify the resistance, but it should be a few Ohms.

c-Would the mosfet get hot?

If you short BAT_IN to GND then yes, it's possible. It's the same as a resistor in this case.

d-On this Pinout, which pin should I use to connect a load that will be powered through B0 controlled mosfet : VBAT, BAT_IN?

BAT_IN

e-What would the best pins to use: B6 & B7 for UART, which ones for I2C?

I don't think it really matters? It depends if you need any of the other peripherals handy.