In the pic for the battle for Carthage I had assumed that the small unmasted ships were hemiolos. The Romans used them as transports, and as you can see they carry more troops than the larger ships.

The larger ships I was assuming to be Quadriremes and Quinqeremes which were the backbone of their fleet. But at this point who can say.

It dose disturb me that any of the ships in the battle are equipped with masts. Those were made to be stepped and unstepped for battle. The masts were not meant to withstand the stresses of collisions and ramming.

The 16ers were about the largest practical war ships. We are not quite sure what the number mean though. Eight men is about the largest amount that can effectively pull an oar. It was surely not 16 levels of oars.