
no i think he did possess the cat's body meaning that yes he did kill him coz he grabbed the cat's head and then released electricity, so he could've killed him with just that. also i think that's why he keeps changing back, coz kayden pretty much gave up his human form to merge with the cat's becoming a complete different life form imo

The electricity could have been him scanning the cat's biological data.Curtin didn't have a medium when he transformed into a cat using Kaiden's method. Kaiden's method basically altered his own genes thus making the cat form as his original form as a side effect ,or Kaiden is still recovering and the cat form is power saving mode.

by this then kayden would be able to transform in any cat he saw ("copied") -instead of being stuck with fatty- since he already has now the altered genes. and let's say curtin was successful having copied a neutered cat shouldnt be an issue, again, since he could change into any cat he wanted -but kaiden's face says the opposite

The technique of transformation was incomplete. His genes is already biologically similar to the cat. Changing to another cat form is either impossible due to limitations of the technique or he deemed it as unnecessary. He's already accustomed to his current form, why should he change just because he's fat or ugly? He's still nimble and able to use his ability. Although Kaiden is a narcissist he's not a person who would waste energy just to alter the cat form to look good. It's body modification itself, they copied the genetics of the specific cat. Changing forms means another scan and body alteration which both needs enormous energy and precise control . It's not as simple as a Transformation Jutsu.

I think he didn't copy the cat, remember at the beginning he was injured and found the fat cat he touched it and i think at that time he possessed it(?) cause when jiwoo found the cat kayden he has blood stains but unninjured...and if he just copied the cat then there should be two fat cats since he feed them together with the other cats. Sorry for my english

i was thinking about this too but dismissed it coz cats can go somewhere else in a whim thus only one fat cat... but cats -unless they're dead- do return to where the source of the food is at eventually, but you're right the coincidence feels off that "original" cat disappeared when kaiden was found... lets say it got startled with his encounter with kaiden and thats why he left to never been seen again? but then what about the injuries then?
I think that Kayden didn't transform into a cat in the first place, but he entered the body of a fat cat. Did the story change along the way?