Sure you can, it's called plagiarism and, if the song you've "stolen" the music from isn't in the Public Domain, it's a crime which bears some very stiff penalties.
believe it or not you can sing almost any song to the tune of amazing grace. but my favorite is singing "devil went down to gorgia" to the tune of "ghost riders in the sky".
Yes, thats what DJ's do
I can but I don't know the song your quoting