Thanks your letter，
en.I am not sure with the solution of this problem.
so I could ont give you some information.
For getting started in DFT，I’d be happy to exchange views with you in the future.
：）

you can download the cif documents for different calculations，and then import these cif documents in Materials Studio to see their structural information. Note that for one determinate structure, the conventional cell and the primitive cell can switch one another, following the MS>build>symmetry. so, check it

Yes, the structure for the static and structure optimization calculation can be different. The structure we get from ICSD or user contributions goes directly into the structure optimization calculations.

In order to compute the band-structures lines we show, the structure has to respect a standard outlined in this 2010 paper that all the computational databases rely on: https://www.sciencedirect.com/science/article/pii/S0927025610002697?via%3Dihub
The static calculation has to be done using this same standard since we need the charge density and wave functions to perform the band structure sampling.