For Question 1: In the empirical study, the four subtests were analyzed separately. So the correlation between subtests is no longer need to concern. But in practices, your request is crucial when employed the proposed method.
For Question 2: The traditional PCA is proved that not suitable for assessing response data, especially binary data. Thus some researchers employed the tetrachoric correlation for binary data and polytominal correlation for polytomous data. The paper we read was employed the PCA based on tetrachoric correlation. But surely the polytomous Rasch models are worth to investigate in the future.
For Question 3: The authors mentioned the distribution of item parameters at the top of page 6. But no further explanation on the distribution. I guess it might due to the proprieties of R_1c and thus no significant difference with the normal distribution.
For Question 4: It does!!!!!