I will be having 17 people for dinner, and I will serve a pork roast. Can I partially cook it, wait until it cools, wrap it and put it the refrigerator and finish cooking it the next day?
Yes and no. You can't safely half cook it. You'd be pulling it out of the cooking process at exactly the point where you'd made it more attractive to bacteria.
You can, however, fully cook it and reheat it. This is a tiny bit tricky with a pork loin, since the optimal temperature for a pork loin is actually somewhat below the temperature that's really safe. You'd want to cook it to at least 140, a bit more than is really optimal. The best way to do that would be sous vide, though you can also do it in a slow oven. Other roasts, like a shoulder roast, with more fat, would be more amenable to cooking to a higher, safer temperature.
Cool it down quickly, and refrigerate. Then the next day you can reheat it. There are a number of ways to do this; see Reheating pork loin roast for a party for one example. A different tack would be to preheat the oven to 400, put your roast in it, and turn off the oven. That would quickly put a nice crust on the outside, while gradually bringing the (already fully cooked) roast up to temperature.
A meat thermometer is highly recommended for this. There are too many variables to do it by time, and you want to avoid both under- and over-cooking.
I do not recommend partial cooking of any meat. You risk bacteria growth. Completely cook your meat, and then warm it up again wrapped in foil to maintain juiciness.