Does the crystalline structure affects the transparency of a material?

Answer 1

The type of crystal structure doesn't affect the transparency. For example a body centered cubic structure is no more and no less transparent than a hexagonal close packed structure. However if the block of substance is a mess of many crystal structures stuck together in no coherent order then yes it does affect the transparency.

Transparency is more dependent on the chemical bonds and the particular light that they absorb. These bond energies are unaffected (ok maybe slightly affected) by the particular crystal structure they find themselves in.

Crystal structure however does have a big influence on the index of refraction of light. You can have left refraction, right refration or even both at the same time depending on the crystal structure.