Yes, they do the three separate fireworks shows at Disney every night of the week, including Fridays, unless some special event is taking place that night at the given park. Time of shows depends on the time of year and time of sunset; obviously, in summer, the shows are later in the evening because of the long daylight hours.
The only fireworks show you can actually view without being inside the theme park itself is Wishes at Magic Kingdom. You can view this show around the perimeter of Seven Seas Lagoon at one of the MK resorts like Contemporary, Polynesian, and Grand Floridian.
The other two, Illuminations at Epcot and Fantasmic at MGM are basically only viewable inside the parks. Some of the higher fireworks from Illuminations can be viewed from the Boardwalk area just outside the Intl. Gateway of Epcot, but not much.
There are no fireworks viewable from Downtown Disney as far as I know.