Polished brick color is a good description. Nothing that looks sparkly, but the blur vein you can see in the photo is a milky whitish-blue. The larger black one has a clearish see-through quality to it in direct light. Rather than black it looks filled with blue grey striations. The darker blue black one is opaque.
The more I look at that red stone, it really looks like red aventurine to me. but, the white parts of it confuse me... It looks like it has a slight mirror like quality. Jasper I have does not look shiney, like glazed brick. Instead, my Jasper is a more dull look like broken brick, even though is polished....
[ETA: Aventurine is in the quartz family. Green aventurine is the most abundant color, then red, peach, and I do believe aventurine occasionally can be blue.]
Blue apatite has a see thru quality. Maybe that is what your blackish blue stone might be. I just don't know if apatite gets that dark.
The other dark stone. I keep wondering if that is smoky quartz?
The purple stone: Does the purple part look like die to you? It almost looks like it to me. They do die rocks a variety of colors often enough.