Presence of certain fins and the morphologies of each are determined by the lifestyle of each fish. I use the largemouth bass to present fin structure because it has most of fin structures of fishes.
(Picture of a largemouth bass (Micropterus salmoides) from here)
Caudal fin - used for forward propulsion of the fish.
Soft dorsal fin - may be used for forward propulsion and as a rutter to change direction.
Spiny dorsal fin - used as a keel to maintain fish balance. Can be lowered to increase streamlining of fish (increase swimming speed)
Pectoral fin - used for braking and turning while swimming and may be used for forward propulsion.
Pelvic fin - prevents fish from floating upward when fish brakes (with pectoral fins)
Anal fin - acts as a rudder for turning, may be used for forward propulsion.
(Tail of bigeye tuna (Thunnus obesus). Picture from here)
Finlets - increase speed of swimming of fish by reducing drag.
(Picture of rainbow trout (Oncorhynchus mykiss) from here)
Adipose fin - function unknown. Current though is that it does nothing, but new studies suggest that it may have sensory functions.
No such things as dumb questions here. Always look at your curiosity towards things as a gift. Not all species get to ask the same questions we can. Think of it as a lovely privilege.
Most all fish spend time in an energy-saving state that can be called “rest”, and we might even call their behavior “sleep”, though it is probably different than “sleep” in most land animals. Many fish, like Bass and perch, rest on or under logs at night. Coral reef fish active in the day, hide and rest in crevices and cracks in the reef to avoid being eaten at night. The resting behavior of fish is very different from their behavior the rest of the day. Many minnows, for example, which are very active in schools during the day, scatter and remain motionless in shallow water at night. Many fish “rest” or “sleep” during the day and are active at night instead, but almost all fish sleep. There are some animals that never stop swimming, like many species of shark, however, they HAVE to keep moving to push water through their mouths in order to breathe, and they may still sleep while moving. [**]
But are they capable of REM (rapid eye movement) sleep in the way humans and other land animals can? Very unlikely for various reasons. Their brain’s are not developed like ours nor are they structured to process information like ours so they don’t need REM sleep the way we do. They get into a semi-conscious state that allows them to still keep alert and responsive to outside factors like predators and other ocean life dangers as they rest their brains and bodies for their waking period. So it’s not exactly what one would call a full night’s sleep. There’s still a lot to learn about the way fishes sleep and process memory as these variables change depending on the type of fish you refer to.
And again, no such thing as a dumb question. Keep curious!