How to add a new color?

Sure thing. First you need to declare the color in the .info file as you mention. If it is just a background color, add it to the Skinr styles section where the first line is:

skinr[background-color][title] = Background color

You'll need to add two lines to the bottom of this group, one to set the name of the color (label) and the other to set the CSS class that will be applied to the block. So you could copy the last two lines, which are:

skinr[background-color][options][12][label] = Light Orange
skinr[background-color][options][12][class] = lt-orange-background

Change the number 12 to 13 for both, change "Light Orange" to whatever your color is, and change "lt-orange-background" to the CSS class you want to use. Then add your custom CSS to local.css (if you haven't set up local.css, see instructions in local-sample.css for how to do this). For example, the CSS that sets the style for the lt-orange-background class is as follows, so you could paste this in and replace it with your class name and your color or other styles:

.lt-orange-background .inner,
.lt-orange-background .comment,
.node-top .lt-orange-background .inner,
.node-bottom .lt-orange-background .inner {
  background-color: #FFA85C;
  color: #333;
}

There are some extra items there if you want to use this color setting for comments, or specifically for the .node-top or .node-bottom blocks (to override any node color settings). It won't hurt to do all of them, but for most blocks you only need .your-class .inner. Save all of this, clear the theme registry and go try it out on your block config page. Let me know if you have any problems.

Oh, sorry, that isn't your fault; that is a mistake I made. I've got custom bullets for different block backgrounds, but to use the Fusion/Skinr setting "List/menu styles: bottom border (no bullets)" I had to add some extra CSS to hide the bullets. But I did it just for the specific color background classes, when I should have set it for all blocks in general. I will have this fixed in the next release, but in the meantime, you should be able to fix it by adding the following code to local.css:

.fusion-list-bottom-border .inner ul li,
.fusion-list-bottom-border .view-content div.views-row {
    list-style-image: none;
}

Let me know if that doesn't fix it. Sorry about that.

That should work. The code you pasted in above is missing a closing bracket (}). Is there any chance you just forgot that?

Fixed bullet problem in release 6.x-1.4

@ #6: which man?