If you are cleaning a pot, boil apple peeling in it for a few minutes to remove stains and make it shine. Clean the outside by gently rubbing it with baking soda.
Well aluminum can be tricky to clean. The best thing to do is to purchase a cleaner or polish made specifically for aluminum. something that will clean as well as re-seal it so it won't oxidize.
Good question, the first thing that I would do is wet a paper towel lightly and brush the aluminum down. After that, I would take a dry cloth and wipe it until dry.
You could try using whitening toothpaste. It takes out most stains since it is gritty. The best way to do this is to put some one a paper towel or sponge and work in a circular pattern.