The sure-fire test for dust is: shoot the sky stopped at 22 > Photoshop auto levels > view at 100%. Even if you don't run levels, you still should be able to see the dust at actual pixels.
Haze could be due to something you wiped the viewfinder or lens with (front and back) that has left a residue. Are your photos showing this haze?
I'm not sure about direct sun on your CCD or through your lens, but everything I've read says DO NOT shoot the sun straight on. I do know that looking directly at the sun (even through your camera) can lead to vision loss, so be extra careful.