Effect of nonlinear transformation on digital signal
Your intuition is correct. When simulating a discrete system, the sampling frequency needs to be high enough that you meet the Nyquist sampling criterion at all times, or you'll have folding.


A method I've used to determine the sampling frequency is to assume the signals are continuous, and find the Fourier transform of the system output. Usually you have an infinite number of harmonics, but you can usually identify a threshold after which you don't care about the harmonics folding. What the threshold is depends on your application and how much folding can you tolerate. Usually, harmonics 30 dB below your signal should pose no problems.
You can't suppress the harmonics at the nonlinear transformer's output, but you can filter them afterwards. Note that this will not help with the sampling frequency, since the harmonics are present between the transformer and the filter.
You need to make sure the signal is sampled at a frequency the DAC accepts. You can achieve that by resampling the signal right before the DAC.