Sweetgirl- Welcome to Autopia!
You can probably do the work yourself if you buy the right equipment (polisher, inspection/work lights, microfiber towels, products). It might, however, be best to have a *good* pro get it into shape and then just concentrate on keeping it that way. The problem is finding a good pro. The vast majority of "detailers" are utter hacks who will take your money and mess up your car...sad but true.
So my short answer would be to decide whether you want to spend a few hundred dollars on detailing stuff (easy enough to spend a bundle just on what you need to wash properly) or to spend a bit more having somebody good get the car looking great.
Depending on where you're located (i.e., your proximity to somebody we can safely recommend), that might be an easy decision as there are people who are simply great at this stuff.
The black spots are indeed paint chips. They can be touched up to where they'll be less obvious, but this seldom (in my case, "never") turn out so well as to be invisible.
Sorry this isn't the sort of response I think you're after...a full how-to would simply be too much to provide here. It's sorta like "I have an acre of land, how should I build my house on it?" But then I can go on for pages about just how to wash
Audis have hard paint, and that makes it tricky to get it looking great. And the silvery trim has a somewhat fragile finish so you need to be careful around that. Not the easiest car to start doing this stuff on. (Note that I've had a scad of silver Audis, currently have two.)
I'd see if you can connect with one of the pros here and have them get your car looking great. Maybe you could get a good idea of what's involved from talking it over with them.
EDIT: If you do decide to do it yourself, yeah...we can help you decide what to get and how to use it, so please don't feel like my response is some kind of "don't try this at home" blow-off.