Is the sign for 'death' the same as 'die' or 'dead'?
Yes, the same sign is used for 'death', 'die', and 'dead'. The context of your sentence and your facial expressions will make it clear which English concept you are conveying.
Does it matter which hand starts palm up?
No, it doesn't strictly matter which hand starts palm up. However, many signers naturally start with their dominant hand palm down and their non-dominant hand palm up, then flip them.
What facial expression should I use with this sign?
Because 'death' is a serious topic, your facial expression should be solemn, respectful, and empathetic, especially if you are offering condolences to someone.