its possible to have the kill feed in the chat without having a mod or rustadmin always running on my computer ?
No, and I doubt this will be a feature as it distracts from gameplay and reduces immersion.
Yes, download the program called “RustAdmin”. You can find it here on the forum and it basically uses the console information to automatically create a server message about who killed who. I don’t use it and I don’t like it but hey, if that’s what you want on your server…who the hell am I to judge lol