For the badge, the method I have used is to get some scotchbrite/wirewool and give it a fairly good scrub, before too long you should see the metal powder start to shine through, then I would suggest some sort of polish, I used Autosol which is technically for aluminium but can also be used for brass, I dab a very small amount on to some paper towel and then dab that all over the badge in small spots, then get a nice bit of rag, I recommend an old t-shirt, and give it a real good polish, that should work a treat