how common is it for there to be sentences like 「私、死んでるよ！」or 「これ、怖い」？ is it super informal? any guidelines on when to speak like this?
Omission of は/を (and sometimes に) is ubiquitous in casual conversations, including not-so-serious business conversations with your colleagues.
But if you think naturalness is important, note that something like 私 is usually also omitted along with は.
- 死んでる！ He's/She's/I'm dead! (after you found someone was dead, or after you woke up to find yourself transformed into a zombie/ghost)