I found these two spent cartages at my local range. What are they? What are they used for, and do you have any experience with them.

Over the years I have collected a pile of miscellaneous live ammo. The look old, probably reloads, and questional at best. Is there a proper was to dispose of then safely? Would it be bad to just through them out in my regular trash?

Going out and shooting with my friend is good, and I learned a lot. But I should probably get some professional training. Any suggestions on where I should go here in Las Vegas?