Okay so Annora needs a nickname, I feel it will only be needed when she’s in elementary school before she truly grows into the full name.
Nora or Noor (keep in mind Nora is the name of my cousin’s little one)
Edit: also potentially thinking Nori but not my first or even second choice
I’d use [name_u]Noor[/name_u] since your cousin is called [name_f]Nora[/name_f]
[name_u]Noor[/name_u] or [name_u]Nori[/name_u] are my favorites. I think [name_f]Annie[/name_f] could work too.
Nicknames tend to come naturally so I wouldn’t stress too much about it 
Nicknames sometimes just stick out and come naturally, my niece is called Kazie and we all call her Hazy Kazie cause she always looks hazy.
Rara
I also think [name_f]Annie[/name_f] could work
[name_f]Ora[/name_f] (I know its close to [name_f]Nora[/name_f] but shes the 2nd cousin (I dont know how often you would see them, sorry)
[name_u]Noor[/name_u] and [name_u]Nori[/name_u] are lovely options but a little too close to [name_f]Nora[/name_f], imo. Maybe [name_f]Ann[/name_f], [name_f]Anna[/name_f], [name_f]Annie[/name_f], [name_f]Nan[/name_f], [name_f]Nanna[/name_f], [name_f]Nannie[/name_f], or [name_f]Ora[/name_f] / [name_f]Aura[/name_f]?
I think [name_u]Noor[/name_u] would be best to avoid confusion