Dakhla to Nouakchott
I can answer the Dakhla to Nouakchott distance question.
From the last cheap fuel station in Western Sahara (which is north of Dakhla at the top of the peninsula) to Nouakchott using the new tarmac road is approximately 350 - 400 miles.
It is a little less than this if you choose to go over the desert and down the beach (which is the old route before the new road was built), however fuel consumption will rise because of the soft sand.
You can fill up just outside Nouadhibou, but that takes you 30 miles or so west which might be in the wrong direction if you want to go directly to Nouakchott.
Many travelers stop off in Nouadhibou to pick up insurance, local currency etc. It is a grim little town, but there is at least one campsite.