1) He didn't report the error term of LC parameter. I think the author never think about the influence of error term.
2) and 3) Yes, It is a good future study. the mixture M2PLM for finding the number of latent class and number of dimensionality simultaneously should be adoped better than 2 stages by 2 separate model.
4) Yes, we can look at the parameter recovery and proportion of correct classification by different methods in the simulation study. It is better evidance to proof any method the author proposed.