hey, a lot of cats do calm down when they are spayed. As for the biting, it depends on the cat: If she is biting you when you play with her (ie: ur hand) then use a toy that gives you a bit of reach, as opposed to something you hold directly.
I don't think spaying has any effect on kitten playfulness & mischief. They just have to grow out of it. It will stop her from coming into heat, which can be interpreted as "calming down".
What kind of biting do you mean? Is she biting you in play, or chewing on things (teething)? Teething will stop by 6-7 months or so. If she is playing too rough, make sure you are not using your hands to play with her - use a toy that gives plenty of distance between her mouth and your hands. When she gets too rough, withdraw your attention and leave her by herself for a bit. She will learn that biting you means the game ends.
We never use our hands to play with her. She'll be playing, then just turn to us, tackle and bite. Does she maybe get bored with the toys on a string and want to go after larger prey!? We've tried to stay still, say NO!, put her in a different room, walk away (we can't do that, she'll follow and tackle as long as you walk!) She'll be more calm, and rest by us more often, but her play is getting much more intense as well, you'd think one would increase while the other decreases, is that the norm for kittens?
Well one of my cats gives me "love bites" all the time but you're probably not referring to that. My cats never had biting issues, I'm sorry I can't be more helpful.