I just try to install the featured image widget in the sidebar. As I didn't find the category "featured images" I created this category and added an image to it. But it does not appear in the sidebar ... the headline "featured images" is there, but no image below it. Could anyone give me a hint what I missed to do.

Yep!

Delete the category - deactivate/reactivate theme.

The theme has to create the category itself to recognize it. Also you can rename it after its created. The theme stores the category ID.

Great. Thanks for the fast help again, Leo

Featured Images is working now in my sidebar, but I get all images in a vertical column and I don't find an editing area, where I can edit how the photos are arranged.

You mean the order in which they show? It might be dependent on which order you add them, but I don't know. Generally 6-12 featured images should show...easily seen by the viewer without the order being a huge problem.

I'll be tightening things up soon so they show better as well.

No, I don't mean the order. Right now they show in a vertical column, six images one below the other. But I would like to arrange the six images in three columns and two rows, if it is possible.

OOOooooooOo 
You wanna message microstockman and see if he will surrender some of his CSS to you

Okay I'll try 

Okay, I got a css-code:

           .symbiostock-featured {
        display: block;
    margin-left: auto;
    margin-right: auto;
    text-align: center;
        padding-left: 10px

but it has no effect. I fear I have done some basic mistake somewhere. For example it has no effect if i create a text-widget and insert it in home-page (below content) or home page bottom row.
Leo, you offered some days ago to have a look at my site, when i create an admin account for you. It would be great if you are still willing to have a look and see, whether there is a fundamental wrong setting.

Did you put the closing bracket?

.symbiostock-featured {
display: block;
margin-left: auto;
margin-right: auto;
text-align: center;
padding-left: 10px
}

Yes, i have the closing bracket in my styles.css
I just missed to copy it here.

checking now

.symbiostock-featured.search-result {
    float: left;
    height: 170px;
    margin: 10px;
    padding: 0;
    text-align: center;
    width: 160px;
}

This should work. Let me know if it does anything scary, bad, or weird.

Leo, I just created an admin-account for you ... I hope the password reached you by mail?

Great! That works ... strange enough: it works after copying styles.css in the main theme not in the child theme.
But it has still no effect if I create a text-widget and insert it in home-page (below content) or home page bottom row.
I have set a static page: Parent is Sample Page, Template is Default Template ... anything wrong with that perhaps?

Lets do this to keep it simple:

Its going to be a few days before I put out a new update - and when I do put out that update it will have to include a fix for that issue since many people may wish to organize things like that. In the meantime, you can get away with just having it in the main theme css. Keep in mind if you re-activate your theme for any reason the CSS file will reset.

Okay, thanks Leo