2. Firstly, DIF effect is viewed as the consequence of the secondary dimension (not intended dimension). But we can model the DIF with one dimensional or two dimensional approach. The different is that: the DIF effect is fixed effect in one dimensional approach whereas it is random effect in the two dimensional approach.
3. Mixed dimensionality means the second dimension plays a role in one group but not in the other group. With the second dimension, the measurement variance (or DIF) could be modelled.