Is it alright to make up a genus for a series/story? I'm making a story that reaches to interdimensional creatures, if there is no genus that fits them in our normal world then can I create a nonexistent genus for the species?

If the story is fiction, then yes of course! It is your story so you can do whatever with it

Yes!!

Explanation:

Just make enough, in world, explanations, so they sound like they could even possibly be true

in fantasy writing if your readers have to look it up because they don't know if thats is true or not, you totally managed your goal of sounding legit.

homophonic or a tonal