Can I use this sign for inanimate objects like a dead battery?
Yes, absolutely! In ASL, this sign is commonly used for electronics, phones, or batteries that have lost their power, just as it is used in English. Just pair it with a context-appropriate facial expression.
Does it matter which hand starts palm up?
No, it doesn't strictly matter which hand starts palm up and which starts palm down. Most signers naturally start with their dominant hand facing down and non-dominant hand facing up, but as long as they are opposite and flip simultaneously, the sign is correct.
How do I show that someone died suddenly versus after a long illness?
You can change the speed of the sign to act as an adverb. For a sudden death, flip your hands over very quickly and sharply. For a slow passing, turn your hands over slowly and gently.