Why is the first है necessary?
The sentence is made up of two different clauses नेहा कहती है (Neha says) and वह दिल्ली से है (She is from Delhi). कि joins the two clauses.
Can one skip वह here?
I don't think you can skip वह here. However, you can skip कि here. At least colloquially you can.
You cannot. It is necessary.
If you skip, it does not point out what she's talking about.
वह indicates herself.