1) Anytime you add a featured image to a post with Choices, it wants to use it for all of the various default theme uses. The default for posts is to have the image displayed in one of the slideshow options you choose in the meta box below the visual editor.
If you don't want that big slideshow on the page, but still want the image attached to the post, you can go to the themes template builder and create a new template. Make the template have a Heading (+ breadcrumb), horizontal ruler and then Post/Page content elements.
Each time you create a post, add this template to that post from the dropdown option on the right of the visual editor for "Layout".
2) If you want to use a different slideshow image for the post than in thumbnails, you would need to choose the option in Theme Options>Layout & Settings > "Slideshow behavior on overview pages" for "Display only single image on overview pages and all slideshow images except the first one on single entries".
3) You can try setting the individual image link option in the Featured Media meta box for that image (on that specific post editing page) but I don't think it will apply the link in a widget area. It be better from a usability stand point as well to have a separate link that clearly states it will take the user somewhere else.
4) Not that I know of no. Only those listed in the dropdown when choose social Icons are available with this icon set.