I'll be in Mauri with a group of bikes in about three weeks time.
The Atar region is fairly close to where there's been recent 'terrorist' activity and the murders of an army patrol. I'm not saying don't go there, but just be aware that security checkpoints could be cumersome in that area as the police and army will still be 'twitchy'. I would probably think carefully before going there myself, mostly because of the likelyhood of additional hassle from army checkpoints. There is also little doubt that some fairly dubious characters have operated in the area, so stay alert if you travel there.
However don't be put off Mauri. I can't recall problems ever being reported on the north south road from Nouadhibou. The people are mostly great, the desert is awe inspiring and I've never felt threatened. I was there early this year, a couple of weeks after the much publicised killing of a French family and encountered zero problems.
Advice re Rosso border is simply don't use it. You need to be pretty focussed to use this border as it can be extremely intimidating. If you want to give it a go, it's best to attempt it at the crack of dawn (before the guy in charge of customs, and therefore scams, wakes up).
As for getting through without paying money, good luck! I went through it once. I paid very little after negotiations, but it was very time consuming. Refusing to pay anything would probably result in a wait that could span many hours or in some cases, days. These guys are experts in the hustle game and to be honest if you refuse to pay anything they'll think you're wierd and pile on additional delays/problems (even the locals pay something - how do you think that customs and police officials earn their money? Take a European head off when considering these things. Border officials mostly don't get much, if any, salary for the job; it's this that fuels the rotten scam culture that exists at every level, where some jobs are 'opportunites' to earn money rather than salaried positions).
The trick as always to to balance a possible willingness, if it becomes necessary, to pay a small tip or a 'fee' for services against allowing yourself to be ripped off by the opportunists that exist in these places.
Go to Diama. What you do is travel to Rosso and as you enter the town there's a fuel station on the right. About 100 yards beyond this is a turning on the right down a dirt road. There's often an army guy there who will point you in the right direction. Keep your eyes open for the turn off; go too far and you'll arrive at the Rosso border post and ferry port.
There's 100 km of pretty reasonable piste through possibly one of the most oustandingly beautiful national parks in West Africa before you arrive at Diama. There are very few (if any) hustlers at Diama and a fairly relaxed procedure. You pay a small fee to ride/drive in the national park before you get to the border, (but don't get ripped off, this should be cheap) and there's a local 'tax' of a few Ougies to pay before leaving Mauritania, again don't allow yourself to get riped off (you get a receipt). On entering Senegal there's 'fees' for the police (about 10 euro and a 5 euro fee to get your carnet stamped). They give receipts (even though it's probably still a scam). It should not cost too much to get through. Don't pay more than 5 Euro to the guy who looks after a 'gate' at the Senegal end of the dam (he'll ask for 10 Euro). This is definitely a scam, you can try and get away without paying, but again, good luck.
If you don't have vehicle insurance a very pleasant and friendly woman sells this from a large tent just behind customs. She'll make you a cup of good coffee, or sell you soft drinks or a

and then proceed to charge you a premium price for insurance. It's all very polite.
Unless you've bought insurance in Nouakchott, then you can't avoid this - about ten miles down the road is a police checkpoint and the first thing they ask for is:- insurance!
(BTW, this woman sells insurance that will cover you for all of West Africa)
Enjoy Mauritania, it's a terrific country with very dignified and friendly people, though with heart breaking poverty.
We'll be at Zebrabar on 20th November. This is a travellers auberge just south of St Louis, Senegal and the most wonderful place for a respite. If you're in the area at the time look us up for a

!
Regards
Craig