My tour was arranged with La Gueila Voyages (
http://lagueila.com ). Its also a guesthouse (auberge) in Chinguetti run by a French woman.
I'd strongly discourage doubling back to Noakchott, as its a lot of extremely boring driving, and when you add in all the police checkpoints (expecting fiches), you will waste a lot of time. But to answer your question there are no marked or signed roads other than the few paved/sealed national roads. Once you go off pavement, you're on your own, and at the mercy of your GPS. The route from Choum to Nouadhibou is actually one of the few that isn't too bad, as you always have the actual railroad tracks to follow (plus it even has distance marker signs). I'd say its somewhere between "well marked" & "good luck".
Everywhere else there are no obvious indicators, and the terrain can get difficult, or impossible without warning. I'm not just referring to deep sand dunes, but mountain ranges, cliffs & canyons, all of which will frustrate you, if not add significant time to your travel if you don't know how or where to cross them. This is "are you crazy" territory. If you break down, it could be days, weeks or who knows how long until someone else comes along (and that someone else might be some nomad on a camel who may be days or weeks away from returning to civilization to call you assistance). Its not for no reason that Mauritania is generally considered to be one of the last traditional Saharan societies. You need to have a ton of experience, not just in the desert, but traveling through Mauritania to have the skills & knowledge to survive there.
As for Senegal, I rode a KTM motorbike south from Dakar, through Gambia, all the way to Bissau. Most of that route was well marked, and is fairly easy to follow (or at least a GPS will get the job done) I'd be happy to answer specific questions that you have.
I want someday to find myself in a desert (with enough water supplies, of course) and in a car. By the way, I understand that the Internet connection in the desert absents. But what about Mauritania in general? Do I need the 