Can the carousel arrows be smaller, without a box?

Yes. In your site's CMS, open Theme, then Advanced, then Buttons & Arrows, and set Arrows to Minimal. The previous and next arrows on every carousel, including the home banner, then show as the arrow alone with no box, in the color of what they sit on (white over a photo), and come to full strength when a visitor points at them. Boxed, the default, draws them as a small box in your button style. Save the theme to apply it across the site.