The Application Process

Hello sir. You certainly CAN address multiple things in your Aditional essay.
whether you should address these specific things is another matter.
To answer your specific questions:
1) Why I don't have my current direct super visor as a recommender (she's brand new)
Good idea! Run with it.

2) Out of my 730 GMAT score, why is my quant score so low? (Q45 V46)
I don't think it's necessary. Yes, people often have higher quant and lower verbal. But you have a perfectly balanced score.

3) Why I don't have substantial EC leadership?
Not a good idea. It's far better to show as much leadership as you can in your essays and not bring this to their attention.

Hope this helps!