When it comes to the remaining part of the Sahara which is under the control of the Sahrawi Arab Democratic Republic, that area is not open for any visitors.
Generally, visiting Western Sahara is considered to be safe, especially Erg Chebbi dunes, near Merzouga. However, it is recommended to check for the latest information on safety.
You can fly or use a bus, car, train, and boat to travel to Western Sahara. However, please, be sure that you have done all arrangements if you go there by car.
Yes, it is possible. You can fly from Canary Islands (Spanish).