Mostly about birdlife, shifting dunes and fresh water lakes, the latter in their best between May and September.
Motor vehicles are not allowed in the park, however, many agencies will offer 4X4 tours. These seem the best way visit the dunes - you have a guide who accompanies you (though I failed to find an English speaking one, so brush up on your Portuguese!).
The shifting dunes with the lakes in between are most spectacular at low sun, when a range of shadows come into play. Just after sunrise is probably the very best because of lower temperatures.
Flora and fauna
Dry sands don't cater for much. Some tiny fish in the lakes along with very small amounts of pond weed, the occasional bird and some bushes along the rim of the dunes.
Best time to visit is May - September, after the rains, and before the lakes dry out. The almost constant breeze may fool you into thinking the sun is not getting at you so be super careful and remember to constantly apply sun screen!
No such thing.
No motor transport inside the park, but plenty around the perimeter. No real roads though, so you need a good 4x4. Horses and donkeys are alternatives.
Trek across the dunes, swim in the many lakes and ponds, be dazzled by the beauty, listen to the silence of the area.
Most people sleep in Barreirinhas and do daytrips. However, the dunes are far more accessible if you stay in Atins, or even better in Canto de Atins. Mandacaru and Caburé are less convenient alternatives. Paulino Neves offers proximity to similar sights (Pequenos Lençóis), although not inside the actual national park. There is also the little explored town of Santo Amaro on the park´s western rim.
No restrictions so far, but there is some talking, due to garbage left behind. Do your part!