DNA's physical properties
Regarding first of two questions:
Assuming duplex DNA (dsDNA), the molecules should repel each other and thus stay in solution at low ionic strength, such as in Tris/EDTA buffer. This is due to the abundance of negative - repulsive - charges. Increasing the ionic strength of the solution, such as high concentration of sodium acetate should neutralize the charges and allow the dsDNA fibers to sediment. In fact, a controlled sedimentation condition may help crystallize the nucleic acids.