Most adult buns don’t like being held so spaying or neutering would most likely not help in this respect. Baby bunnies though are always okay with being held. So I’d say this is completely normal and you shouldn’t be picking her up unless it’s absolutely necessary from now on.
Nipping may or may not be caused by hormones, so depending on why your bunny nipped, spaying her may or may not help. Bunnies nip as a form of communication too, so if she nipped you when you were trying to pick her up, that’s her way of communicating that she didn’t like what you were doing. My bunny nips me lightly sometimes when I’m in the way (e.g. if I am sitting in his path and he wants me to move). There is also the hormonal nipping where the bunny just nips in aggression because they are hormonal – in which case spaying or neutering would help.
The same goes for chewing – many fixed buns will still chew. It’s just a general bunny thing to do, which is why people still bunny proof areas where the bunny will be in even after they are fixed. If the destructive behaviours are caused by hormones though, then yes spaying would help
Regardless, it’s essential to spay female bunnies because of the high risk of uterine cancer.