This looks like a setup for a 'headcannon' pun.
I always saw A:CTS taking part in a period of rapid technological expansion similar to that of naval tech around the American civil war; when a ship was completed, the technology it used was already out of date. This theory is supported in game by the coexistence of wooden and ironclad ship hulls along with that of steam-powered propellers and sails. Therefore all the bases are covered for both Muzzle-loading (as in the cannon sprite at first glance and round ball projectiles) or breech loading (as in the shell sprite used to represent ammo and Large Cannon sprites) depending on how far along military technology is in your headcanon / game of conquest.
As for caliber, Zark posted the official pixel to meter conversion ratio in the forums somewhere I can't find, but I'm guessing based on the size compared to a sailor that they're pretty damn huge, and they'd have to be to wreck fortifications like they do so quickly.
Yeah, pretty much. It's the kind of rapid evolution you got in the late 19th and early 20th century, where sail-powered wooden-hulled ships firing broadsides got replaced with coal-powered steel-hulled ships with far larger turreted guns - via a bunch of weird and often kind of awkward stages.
Ohh... thanks much! :D