The carronades from around 1784 (i.e. very soon after development) got a notched foresight block to give the line of metal (roughly 3 degrees) as well as two other intermediate elevations (no high quality measurements or images to scale, but I'd assume 1 and 2 degrees) and the fully disparted line of sight (e.g. no elevation). Accurate use of sights takes longer than only lining up the top line, but this necessary step would significantly improve accuracy as long as you could persuade gunners (and the officers on the ship) of the importance of sights... This was an uphill struggle until the 1820s though, with Nelson being very against sights, and not untypical).

Guns of the naval pattern tend to be close to 1 degree line of metal.

Field artillery *did* use sights extensively, notably also tangent sights to provide a point of aim out to 1500-2000 yds depending on nature. Navies were a little slower in taking up sophisticated sights - relying on the top line, and quartersights or quoin/bed elevation marks. This is in part a consequence of the unsteady platform, but this was compensated in it's turn by the density of ordnance deployed (Waterloo, with ~50,000 men had only 28 artillery brigades or troops ~ roughly the same number as on three first rates, and all of 9pdr or smaller guns, or 24pdr/5.5" howitzers...

As to firepower. Carronades are always at the upper end of the calibre range for a given ship (a First rate armed with 32pdr, 24pdr and 12pdr guns will carry 32dpr carronades (rarely a smaller number of 42 or 68 pdr pieces), while a fifth rate might be armed with 18pdr and 9pdr guns and 32pdr carronades.
Carronade ball has no 'special' character compared to that from gun of the same bore, and the use of reduced powder charge and double shot can give guns a lower muzzle velocity than a carronade - as well as permitting single shot to be fired at a higher velocity in the approximate ratio of around 15:9 - which can be used to obtain a marginal penetration to an extended distance, or to obtain similar penetration from a smaller shot.
A 32pdr carronade will penetrate to a similar depth as 18pdr guns at typical combat ranges, with a larger 'cutting' distance (6" vs 5", roughly, which is similar to the relative degree of rigging damage and injury to framing). The 9pdr that stand in the same battery will penetrate less well except at extremely close ranges, and will make holes only 4" in diameter, cutting less rigging, and injuring less framing.