Semolina is definitly not whole grain. It is simply the endosperm of durum wheat, a hard, high protein, variety of wheat. The bran layer and germ has been removed. The endosperm has more of a yellowish tinge than spring wheat, and various varieties of hard winter wheat commonly used for bread, which I believe is called farina, but I'm not sure, but it is basicly the same as the wheat flour used for bread. It holds together a bit better than farina, when boiled in water. Since it used to be more expensive than farina, many years ago, some pasta was made of a combo of farina and semolina, while the "premium" brand where all semolina. Today there is not much price difference, and most pasta is made from pure semolina. Durum wheat can be acquired whole, as in whole wheat durum wheat pasta. This is not semolina. It is whole durum wheat including the endosperm, germ, and bran.
Both whole durum wheat, and semolina, themselves contain no animal products, thought it is possible that some of the vitamins commonly added to them, may. I don't really know. And no, ferrous lactate -- the lactate portion is not made from milk these days. It is made from carbohydrate fermentation. So there is no point in avoiding pasta with ferrous lactate added, in preference for ferrous gluconate -- not sure what that is made from though.