I think Prada Sport is more casual but incorporated into the Prada main line as a wider selection of nylon jackets. Even though Prada Sport does things like fur lined vests and hooded trenches, the fur they use is almost always fox, rabbit and goat fur. The collection is mainly of black coordinates and separates, always shown apart and separate from the Prada Main Line Collection. Thats my 2 cents
As for Linea Rossa I have no idea, I think it has something to do with Prada's Sailing Boat