Switching 4.2V circuit with 3.3V Arduino GPIO I am trying to learn about MOSFETs and see this p channel MOSFET and this tutorial.  I am trying to use a 3.3V arduino GPIO pin to control a load that is powered from a 4.2V battery in much the same configuration as the circuit drawn in that tutorial.  Most other tutorials I see say the Gate Voltage needs to be equal or greater than the Source Voltage, but the tutorial I cited describes that actually the Voltage between the Gate and Source just needs to be more negative than the Threshold Voltage.  The P channel mosfet I cited is Vthreshold -2V to -4.  So my question is whether this P channel MOSFET would allow me to use a 3.3V arduino GPIO to control whether that 4.2V source is closed or open to the drain/load.  Looking at how that tutorial does the math, it seems in my case the GPIO being off would mean Vgs is 0 - 4.2 = -4.2 and therefore the MOSFET is in the ON state.  If GPIO is on at 3.3V then Vgs is 3.3 - 4.2 = -0.9 and therefore the MOSFET is OFF.  However, the tutorial doesn't say what happens when Vgate &lt; Vsource but by an amount less than the Vthreshold so I don't know if my math is right.
In sum my questions are:

Is my math and prediction of the MOSFET states correct when that 3.3V GPIO is on or off?
If not, is it because of some other quality in this MOSFET and a different P MOSFET would work?
I presume that if I keep out of the Vgs upper and lower bounds then I avoid issues where the MOSFET is in a partially on and partially off state, is that correct?
Is it just impossible to use P MOSFETS in this way?

Note:  My questions only pertain to P MOSFETs.  For my project (switching a 1-2A disco light toy), it has to be a high side switch and that's even besides the point because I am more importantly trying to understand how the P channel mosfets work.
The MOSFET you chose will probably fail. Using a 30V device on a 24V system is asking for problems. Go to a minimum of a 60V MOSFET and use a UIS, Avalanche rated one. R4 is very week for what you need to do, I would suggest something in the 10K range to swamp out any leakage in the Arduino. If the MOSFET is properly rated the flyback diode is not needed but make a space for it incase you have to sub a MOSFET. Putting C2 in parallel with C1 will help. I do this a lot with electrolytics. I double up each one the needed size when one fails you don't notice it. I would suggest a couple of 220nF caps across the motor but that is application dependent.