So I understand, a FAC is anything in between 500 and 1000 tonnes.
Is just purely a cosmetic name, or are there any special rules for FAC (except not needing a bridge?)
No, the only technical difference between a ship that is 1000t versus a ship that is 1100t is that you will need a bridge on the latter. You may call whatever ship you wish to be a FAC or whatever...
I usually call "fighters" for crafts or FAC (Fast Attack Crafts) 125-750t, ships between say 750-1500 is a boat or vessel commanded by a minor officer such as Lt. Commander. I really don't distinguish weight as much as I do missions, even though a Corvette generally are smaller than a Frigate and so on...