What happens when you connect a 16bit analog device to a 10bit adc
You mean an analogue device with 16-bit equivalent SNR/resolution? (analogue doesn't have  discrete steps) It will simply be sampled at 10-bit resolution by the ADC. 

However, you can use techniques like oversampling, averaging and dithering to increase the resolution to more bits. Very roughly, say we have a one bit ADC with a step of 1V, and you have a signal that is at 0.5V - the ADC will report 1 half the time and 0 half the time (noise will make sure of this). If we take lots of samples and average them (add them all up and divide by number of samples) we will get around 0.5. The more samples we take the more accurate this will be, the downside is the highest frequency we can see goes down, as we are in effect creating a (digital) low pass filter. 

So yes, it will still function. Sorry I can't help with the exact details of interfacing as I have never used an Arduino, although it will be a case of "input signal to ADC pin".