How My Mother's Prediction Came True, As Told Through A Cryptic Crossword

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Across
  1. 3. I have Shakespeare's determination (what makes you think I will allow you the same?)
  2. 4. The first alphabet (is what you'll never be)
  3. 5. Short buzz-cut (is better for me, I don't care if you prefer pigtails)
  4. 6. The first year of us
Down
  1. 1. The essential munchkin, gross, obtain friendly core (as if that's going to help you to feel authentic)
  2. 2. Not quite all, en route, singly