Don't worry about alpha nonsense.
Your puppy is being a puppy... puppies bite, play rough and hard. If she bites too hard, simply yelp (like a high pitched 'Ow!' or something). If pups are taken too young from their mother, they often don't learn proper bite inhibition so it's our job to teach them
I consider Jackson an equal to me. I am not above him nor do I force him to do anything or consider myself an "alpha"... he's my best friend, my partner, we work together as a team.
Here is some of what we have accomplished through positive reinforcement and clicker training:
I would check out youtube channels zakgeorge21, kikopup, pamelamarxsen, etc for some good training videos.