I know that unused op-amps that come in multiple packages should be terminated or they could potentially produce noise. Is it recommended to terminate FETs in a similar way?

 

More than recommended, I would say mandatory. Without connecting the source and gate via a resistor the transistor will open if the gate is left unconnected, either fully or partially, and will be very susceptible to EMI. If it opens partially and is used as a high power switch it may also overheat and get destroyed.

 

Yes. You should have the gates connected to the sources. FET gates have such high impedance that static electricity fields that you wouldn't even notice can turn them on, where they can drift in some stage of conduction for hours. Conduct to what? They aren't connected to anything.

Yes they are. They must be in a chip with several transistors or you wouldn't have extras. Play it safe. Put a leash on those extra dogs.

 

Even better, tie the gate to drain, and connect source to Gnd.

 

Great, thanks for the feedback. Source grounded and gate tied to drain.