1) I also think why not he estimated the number of latent classes and dimensionality simultaneously.
2) BIC usually has good performance. AIC criterion tends to overestimate the number of classes.
3) Yes, I think it just roughly correspond with the trend he discribed about the characteristic of these 9 classes.
4) Yes, the MNSQ index could be tried to use in this process. It is more reasonable method to reduce items.