Show images for member levels?

Is it possible to show an image next to an author’s username, or below it? For example, I have free members and premium members and would like to be able to show the member level on post the post page and BuddyPress profile by using an image, similar to vBulletin ranks.

Yes. s2Member doesn’t handle how things appear on your site. That’s for your theme. So you would need to modify the relevant templates in your (child) theme, or else find a plugin that does that for you.