Thanks to a few questions by Ali, there is a good discussion of question 2 from 2005 on a previous thread. See here..
This describes at least two ways to see the answer to this problem. Let me know if it isn't clear.
In that problem it can be thought of as an issue of whether effectively it is a monatomic chain or a diatomic chain. Or it can be thought of as an issue of what wavevectors of scattering are allowed. (Note the examiner report says that no one got this part of the question!)
Regarding the solution of q1, 2010, the point about rotation and translation: What I mean is that you can line up each atom from the unrotated-untranslated crystal with an atom of the rotated-translated crystal. Does that help?