I am not a gemologist. That is what you need to see. It will cost you a few $ to have each stone checked/appraised/accurately weighed. But if you plan on selling, you will need that information for each stone.
Seeing that I am NOT a gemologist, I'd suggest your stones include: diamond, citrine, cubic zirconia (CZ), sapphire, ruby, emerald, garnet, aquamarine, topaz, amethyst, possible tanzanite, and several others not known to me. That's why you need a reputable gemologist's opinion on each stone. Be VERY careful of that violet/purple stone!!!
Ask for an appraisal for insurance purposes on each stone as well. Make sure you get each stone back individually labelled. I'm not certain I would take the whole lot in at one time. Be sure to take detailed photos of each stone before you submit them. Demand a written receipt for the stones, including the photos if possible with the receipt. Prepare the receipt for the stones before you enter the store or premises. Have the gemologist sign for the stones, along with a witness if possible. Need copies of the receipt for future reference if you don't get everything back.