I've been studying crystals and stones quite a bit this past year and have some good reference books in addition to testing many of these out myself. It's fascinating how many of these work. Some don't do anything for me but other empaths rave about them. While others are like medicine for me and have really helped me with various emotional, physical, and spiritual issues that I had been having. I'm happy to share a few notes on several you listed:
Hematite is a pretty good protection stone that brings you strength, love, and courage.
Smoky Quartz is supposed to be good for removing negative from you to help you stay grounded. It is also supposed to help you connect better with the spirit world if you choose to do do.
Carnelian is known as the "feel better" stone and is a good all around stone to have on you to better your health. It is supposed to help you see the connection between the emotions you take in and put out and how that may be impacting your health.
Malachite is supposed to calm you down and bring peace of mind.
Turquoise is another "feel better stone" and is supposed to speed up healing of many things that may be wrong with you (colds, flu, stress disorders etc...). It is also supposed to provide you with mental and spiritual clarity to your life path.