I haven't read all the other posts carefully -- I'll just say this quickly --
I use an elderly Nikon D70, a Panasonic point-and-shoot, and my cell phone camera. You don't need to mortgage your house to have a camera that can take good product photos. My preference for close-up product photography is a camera that I can use in manual mode so I can keep the F-stop (field of view) at a constant setting and can easily adjust the exposure time. That's usually the D70, but the Panasonic works in a pinch.
The main source(s) of light should light up the front of the soap, not the back or sides. This main light should be angled so there is a slightly brighter side so the image doesn't look flat. There should be a a secondary source of light coming at an angle from the other side (this could be a reflector or an actual light). Misschief's bar with translucent embeds is an exception to this rule, but even with that soap, the front should still be adequately lit.
Shoot several photos with varying shutter speeds so you can pick best exposure. Most of your shots are slightly underexposed (not bright enough). I would prefer a longer shutter speed for most of the photos you shared in your first post.
The soap should be the focus of the image. I often use a white background, but that's just one possibility, but keep it simple and clean.
Zoom in on your soap. If you're selling, the soap should nearly fill the frame so people can view the product. That said, you also have to keep in mind how you will be using the image in your e-store. Will your images need to be cropped to a square or a rectangle for use in your e-store? Keep that in mind so you can arrange the composition of your photo and zoom in accordingly.
Here's a typical setup that I use for product photography. There are 3 sources of light -- Light 1 is the main light that shines onto the front at a slight angle. Light 2 is a side light to add brightness to the corners and one side of the arrangement. The reflector softens the shadows on the other side.