No reason to put semolina or cornmeal or flour directly on the stone, unless you're starting with a cold pizza stone. If you're sliding the pizza off a peel onto a hot stone, though, you'll get plenty of semolina/cornmeal onto the stone as it slides off. When I first started making pizza, I used to open the oven and throw cornmeal on before putting the pizza in, but it made no difference in sticking, it wasted cornmeal, and it smoked up the kitchen. (I've since switched to semolina, since it's a more neutral flavor.)
Pizza stones work perfectly well with store-bought refrigerated dough as well as home-made. They also will work with frozen pizza as well, though I agree with another answer that suggests starting with a cold stone rather than a preheated one in that case. (I'm not sure how much benefit the stone actually will give in this case.) I rarely make frozen pizza these days, but I once tried an experiment with preheated stone where I turned on the broiler above the stone for five minutes before putting in the frozen pizza. The stone cooked the frozen pizza crust quickly, and the broiler heated the toppings. It wasn't quite done evenly, but I can imagine that this can work if you want to cook a frozen pizza fast.