Can different storefronts have totally different designs?

Yes. Theme assignment is scoped per store-view, so each storefront can have its own theme, logo, colour palette, fonts, header, footer, even checkout layout. Most clients use one parent theme with per-storefront skins (cheaper to maintain, faster to build, easier to upgrade). For radically different brands — e.g. a luxury sub-brand vs a discount sub-brand on the same backend — we deploy fully separate themes with shared core blocks. Hyvä supports this pattern natively.