1. Formamide and/or urea most likely. They both lower the melting point
    of the ssDNA. This allows the structures to unravel at lower
    temperatures. Typically you want to reach for  melting temperatures
    around 50° C, and then run the gels at that temperature. RNA is
    often denatured with harsher agents, like formaldehyde because RNA
    form stronger structures.
 2. ds DNA can exhibit supercoiling which is a very elegant method of
        packaging DNA. This is a huge topic and mathematically derived. It's
        important is mostly due to it's role in gene expression via the
        interaction dsDNA has with proteins it wraps around-his tones.

Note that ds-supercoiled-DNA forms two structures; a plectoneme or a toroid, and can also have combinations of these two. It's interesting stuff. Google "DNA supercoiling" with an image search  and look for a figure that shows the different levels of winding and wrapping:

I'm not very familiar with [this source](http://click4biology.info/c4b/7/images/7.1/DNAfibre.gif) but the figure looks to be on the up-and-up.

Good question