Is it possible to measure the voltage and current of a load with this circuit and Arduino?
In your circuit:



it is, in theory, possible to measure the voltage across and current thru the load.  The voltage is IN0 - IN1, and the current is IN1/R.

However, for a useful current measuring circuit, R would need to be very low.  You want the worst case voltage dropped across R to be a small fraction of the total 12 V that is available.  You don't say what the maximum current is you need to measure, but I'd start with not wanting to have more than 100 mV across R.  In reality, that means you need to amplify the IN1 signal before presenting to a A/D that has a 5 V or 3.3 V input range.

Another option is to use such a high resolution A/D so that you still have enough resolution left after using only a small portion of its range.  With a 20 bit delta-sigma A/D, for example, with 3.0 V reference, 100 mV would be 1/30 of its range.  That still leaves about 15 bits of resolution.

As for IN0 being a higher voltage than can be measured directly, use a resistor divider to scale it down to the range you can measure.  For example, a top resistor of 20 k&Omega; and a bottom resistor of 10 k&Omega; attenuates the signal by 3.  If using a A/D with 5 V range, that means the input signal can be measured over a 15 V range.