1. Add the parapeter link=”file” to the gallery shortcode
2. Add the image’s id to the exclude parameter of the shortcode. Alternatively don’t attach that image to the post. See more here.
3. In style.css change the background value of .gallery-item
4. You have the column attribute for the gallery shortcode, see the link above
5. Static links is the classic Next/Previous pagination, AJAX has a “Load more posts” link and Inifinite scroll automatically loads new posts when the page has scrolled to the bottom.