1. I think it is intuitive the DIF items should be investigated in between-person level first. After that, the DIF items between school-level are investigated then. In most complex situation, the DIF occurs at both between and within levels. It is worthy to do for the future study.
2. Only one DIF item was considered in this study. Multiple DIF items should be included for future study.
3. Study 2 adopted an approximate multi-group multi-level model instead. To free this restriction, a more general estimation such as MCMC is more suitable than using Mplus.
4. In within-level DIF analysis, it seems like an unnecessary study because it is just a common DIF analysis (within-level analysis). The multilevel strucuture aims to include high level variable (school). When a wrong model is used (CFA), it is not surprising the parameter estimation is bad.