interaction of grape juice or wine with marble
CaCl2 and magnesium are not toxic at these levels. In fact NIH suggests around 1 g calcium per day: https://medlineplus.gov/magazine/issues/winter11/articles/winter11pg12.html

Marble itself is predominantly calcite or dolomite, that is carbonates of calcium and magnesium. Marble also contains other elements. We can't say if these other chemicals are safe just by a photo because composition of marble varies. 

When you bought this cup - did they say it is safe to drink from it? Supplier should know if the material is safe or not. If you didn't get assurance that it is safe then you should assume it is not.