Its always very hard to accurately tell what a stone is from a picture.
In that last picture the pink stone looks more like Rose Quartz. The wonderful blue stone makes me think that is Chlorophane Fluorite. did you use a flash or any artificial light to take the pic? It seems to be flourescing  Do you know the mines name? That way we could probably be more accurate.

You could polish the stones with grit papers that are quite easily available, starting with a very rough then going through finer and finer, but to be honest you might do more damage than good, and they look rather beautiful as they are

the name of the mine is the hiddenite mine if i'm not mistaken they have a total of 62 different gemstones can be found there oh and yes i did use a flash i'll take some more without it and see how they turn out

Lolol doesnt narrow it down much then does it !

no not by very much guess i've got quite a few pics to go though i'm still messing around with the settings on my camera to try to get a good picture without using the flash but so far it doesn't look good. lol

North Carolina's hiddenite area is rich in rocks & gems.  You definitely have citrine and amethyst, Lower right is flourite quartz.  Lower left appears to be aqua marine quartz. Second picture - The blue with gold speckles is lapis lazuli. The blue green is turquoise.  The larger stone appears to be raw rhodolite quartz.

As far as cleaning, use a mild liquid soap and water. Pat dry and use a sesame, almond or canola oil and rub stone well in your hands. use a soft cloth to wipe off excess.

To smooth out edges use a soft grit sanding paper or a buffing block for finger nails. If you want a more polished sheen use a tumble filled with sand on low. Hope this helps.