Hello there Daniel, and welcome to Essay Forum!
As I'm sure you knew coming into this forum, there's no magic answer or secret formula that will suddenly transform you into a wonderful writer. This forum can help you, though!
One of the great things about an academic forum such as Essayforum is that it gives you the opportunity to see the emotional feedback and response that your essay creates. This in turn helps you to become a more confident writer, something which is essential in developing your writer's voice.
Allow me to address your specific questions:
how can I identify if I am writing at the appropriate academic level?
Writing is unlike other academia in that it is equal parts art and technique. This means that every academic level will have extremely variable writing samples. It also means that writing is very hard to measure- art is oftentimes interpreted differently depending on its audience. Fortunately for you, Essayforum is a great place to try your work out on many people and get a feel for its effect. I would also recommend against comparing yourself to any academic standards- instead, strive to make your writing the best possible. Don't get hung up on right and wrong- even this short introduction proves that your writing technique is solid, and well beyond that of "a child in elementray school"- concentrate instead on clarity, precision, fluidity, and emotional effect, when appropriate.
How do I know if my writing is mundane, or exceptional.
Post it here! We'll let your know. A disclaimer, though: many here on this forum like to give out compliments. I would make it very clear at the head of each essay you submit that you are looking for straightforward, honest advice. This makes a difference.
how do I master writing at the graduate level?
Practice. I hate to break it to you, but there is no other way. In coming here in the first place you've proven that you are looking to improve. That's a big step in the right direction!
As a forum user, I should warn you that not everyone here is a graduate or even university level writer. A few of us are, and many of us have a very solid grasp of the English language. EssayForum also has a great staff of accomplished moderators who will check every thread. Between these authorities, you will get solid advice on the grammar, structure, and specifics of good essay writing. From everyone else you will get feedback about the art aspect- that's the great thing about EssayForum. There's a place for everyone.
There is one other positive aspect of this forum which will help you reach your goals: the exposure to other writing samples, good and bad, is essential to establishing your technique. In good writing you'll find inspiration, in bad writing you will learn what to avoid, and in all writing you will gain perspective. Take advantage of the diversity here!
To get started, I would encourage you to poke around the forums and then to post a few of the assignments you're unsure of. We'd be happy to take a look!
Have a nice one.
Tim