1. No. The slider works the same way with or without a static home page.
2. Create a category for posts called "slider" (or whatever), add a post to that category, and add a featured image to that post. In Graphene slider options, set it to display posts that are only in the "slider" category.
If all you really want to do, however, is display photos, Graphene's built-in slider probably isn't what you're after, because it's meant to highlight posts. You may want to disable it and use a slider specifically meant for images (of which there are tons).
Moved to Support.