From what I have seen, the base reality works as:
Weapons have a property called "firerate", and interval between activations goes as 1/firerate. Thus, the ubiquitous "3.7 per second" is from 60/16 = 3.75, truncated to the tenths place. I suspect that the weapon optimizer rom works as 80% * firerate, so a 3 (60/20) weapon goes to 3.7 (60/16) and a 12 (60/5) weapon goes to 15 (60/4).
They also have a property called "lifetime", which explains why some fast projectiles don't go as far as some slow projectiles; for instance the laser cannon (1 * 30 = 30) vs. the Mk 5 howitzer (.5 * 120 = 60). Note that each value is in double light-seconds, which is why the howitzer can be used to bombard targets up to 120 ls away.
Shield regeneration is considerably more complicated, judging both by
this post on the wiki and personal experience: surely we've all seen odd hiccups in shield regen.