One of the photos in this thread shows the current configuration of exposed suspension components:
(here). Really, only driveshaft and various control arms. Back side of wheel fairings shows some exposed hardware. Earlier P3 version had exposed spring/strut.
True about the exposed exhaust. Current P4 still has the Geo Metro engine. New IAV engine is expected installed in June; then we may see an exhaust system that's closer to production design. Elio has specified 5.75" ground clearance so hopefully they will tuck the visible downpipe up into the bay a bit more.