Hey! Late response, sorry man.
I'm actually in a class that's covering a bunch of this stuff rn, so. Procrastinating on this next exam is NOT going the way I expected so far XD
When making sea life, especially plants, know for sure if it's a plant or an animal. For example, there's a thinner line than you would think between jellyfish and coral in phylum Cnidaria. Sponges are another thing people keep mistaking for a plant. This is a teeny but important, because some sponges/corals are actually predatory (look up the sea harp sponge) and can do some cool stuff because of that. Also, almost ALL sponges/coral/seaweed are mutualistic with tiny animals in order to live. The general working structure is almost always they provide protection and a habitat for the animal, and in return they get nutrients. (Most common example: a lil unicellular animal named Zooxanthellae is the only reason we can have coral reefs.)
As far as naming goes, we have our man Linnaeus to thank for Latin-izing everything. The system was like twenty times worse before that. If you want to go with general names in story instead of making a giant taxonomy system based on one of your ancient languages (which I srsly can't recommend. Bc who has the TIME), I would stick to stuff like appearence/where it lives/what it eats/what eats it for naming different things. Oh, and only green stuff is photosynthetic. So there's that too.
Hope that helped!!