1) I think let them evolve. She'll probably have a ton of nicknames before she's one, and one will eventually stick - or maybe several!
2) Not really. I'd still call her my favourite nn (unless she hated it) and that would be my special pet name for her - nobody else has to use it.
3) Nadie & Deeny seem most natural to me. NiNing is cute.
Nadou,
Dina,
Nida,
Didi, Dida &
Nani (nahnee) all also come to mind.