In order:
What makes someone a professional? Well there is the "A professional is someone who makes a living from the job" answer - which is strictly true, but to me, professionalism is a state of mind. When you get into the 'office', and you put your all into making the show the best it can be, when you treat people in a "professional" manner, and when you demand the same of your colleagues.
What impresses me in a young stage manager? When they turn up early, or at worst, right on time. When they walk into the room confidently and command respect - not because of the position they hold, but due to their actions. When they can approach difficult situations in a clinical manner, solve the situation fairly and without causing too many bad feelings. When they know how to listen as well as how to talk.
The key to growth, in my opinion, is to know your limitations and your strengths, then play to your strengths, whilst making your weaknesses a non-issue. Then as you evolve, try and work on getting rid of your weaknesses.