1. The social buttons don't show up below my articles. They DO show when i view the articles in a category blog, they DON'T always show when I display an article as a single article.

2. Where can I change the settings of the social icons?

1.) Yes youre right, the socials are only at blog. If you want to show the socials at all articles you have to use "K2" or another extensions
2.) You can setup the socials at the template backend parameter