Store it in a dark, coolish cupboard in its original bottle. And, yes, it lasts fine.
Here's what I like to do with it: Pan broil beef or lamb (steaks, chops, even patties of ground meat. Pour off any fat. Deglaze skillet with some Marsala, and cook it down until it's syrupy. Add heavy cream, and -- if you like -- a little prepared mustard, and boil until sauce is thickened. Pour sauce over meat and serve.