1) cute, adorable, lovable, cuddly.
Generally conveying the sort of maternal emotion that a mother would feel towards a baby, and primarily used by teenage girls to refer to something small and baby-like to which they feel affection.
2) Said (or "squealed" is a more accurate word) when the speaker feels the affection described by noony(1) and wants to vocalise this affection. Once again, primarily used by teenage girls.
Person A: Look! A cute Asian girl!
Me: Yeah, that's my Noony.