I just did a conversion and my character has quads. The way I checked that was to set the display option in the Scene Manager in CC to wireframe.
What you are looking at is the display when doing an Edit Mesh. Why this shows differently, I wouldn't know.
As to the resolution, the DAZ character is transformed into a genuine CC character, which will have a lower resolution in general.
Importing via 3DXchange does not change the resolution, but it will triangulate. It is only recent that iClone and CC support quads and 3DXchange has not been updated to reflect these changes.
The result via 3DXchange is a so-called non standard human character, which will still work, but lacks the benefits of using CC, such as putting a variety of clothing on your character.
The emphasis in iClone is more on animation than on creating high-quality stills, so the character implementation needs to be efficient. The look of iClone characters has greatly improved over the years and more is coming, but this comes at the price of needing a more powerful PC.
I hope this helps.