There are two different objects that represent a user in the Stack Exchange API, the full user object and the smaller shallow_user object. Which is returned depends on the method being called, methods that are focused on users return the full object while others return the shallw one.
In the last sentence, change "shallw" to "shallow".
Some badge, like Autobiographer, are held in common across all Stack Exchange site. Others, like most tag badges, very on a site by site basis.
In the last sentence, change "very" to "vary". Also, change "badge" to "badges".