No need. They are to prevent oscillations in high frequency circuits and that's not a problem here
Depends upon the voltage and the MOSFETs used.
As I previously stated, for a 5V supply and 5V gate drive, the MOSFETs need to be logic-level types, with a gate threshold voltage Vgs(th) of 2V maximum.
A pedantic note: when a MOSFET is used as a switch they are not driven into saturation (which is the active region in a BJT) but into the linear (or ohmic) region, as shown below (which is the saturation region in a BJT).
Why the solid-state physicists used the same word for a different operating state in a FET as compared to a BJT is beyond me. Guess they thought they would throw that in there just to confuse the rest of us
And it worked.
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