I understand the terminology in context. It pretty much translates to the self-centric asshole, when you really look at it and what it means. Hence DDavid's posting of James Bond. Though JB works alone typically, so it is hard to say he fall into the 'leadership' role, but he does act in his own self interest when it comes to the vast amount of women he has had sexual relations with in the course of his career.
Not necessarily. "First' in alpha could be a bit more "first among equals". While the term alpha male is associated with very masculine personality traits, these do not have to expressed in a dislikable way.
An alpha need not be a leader who chooses to lead others. He can simply be an individual of extreme self confidence. He will do that which best benefits him or his mission and others can choose to come along. Or not. The alpha doesn't give a crap if they do or not. Not his circus, not his monkeys.