For determining the resistance of the coil you need to measure the voltage across the coil and the current flowing through it (V=IR). You can probably rig up something using some resistors, a couple of opamps and one of the 328's ADC channels, or you can investigate the easy option...
www.ti.com/lit/ds/symlink/ina219.pdf
it's good reading and while this part may be overkill the first page of the datasheet links to a few alternative parts and I'm sure options are available from other manufacturers.
For changing the output voltage, the Naos Raptor datasheet shows a trim resistor between pin 5 and ground. I'm no expert but it may be possible to connect the resistor between pin 5 and the output of an opamp (*instead of ground) then drive the input of the opamp with a filtered PWM signal. With a little experimentation the 328 should be able to drive the op voltage to whatever you desire... Read the op voltage back via the ina219 or a separate resistor divider + opamp + ADC input.
*instead of ground: The opamp output is acting as a virtual ground, by changing this you fool the Naos into seeing what would be different resistances with respect to actual ground. Make sure to use an opamp that is capable of driving its output close to ground, how close? Close enough to work