As I mentioned in the other post, I still have question or two about the simulated data and thought it would be better to start a separate post. Here is a quote of yours:

Quoted from Mike.Linacre Uve, the simulated responses are generated according to the Rasch model with generating parameter values equal to the Rasch estimates from the current data. Consequently, the simulated data are what the current data might look like if the current data fit the Rasch model perfectly.

This makes sense to me. However, what I am not understanding is how the random generator can create responses such that these random responses fit the model as perfectly as possible given the measures for the persons and the items.

Uve, please see http://www.rasch.org/rmt/rmt213a.htm

Remember that "perfect fit" to a Rasch model, is not "observed data = expected data". Perfect fit is "observed data = expected data + expected randomness".