Basic cryptic

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Across
  1. 1. Offers her contact details with even less feeling. (6)
  2. 6. I'm in favour of melody, as luck would have it. (7)
  3. 7. Meet Rex. He's pretty over the top. (7)
Down
  1. 2. Smoothing out the bumps at night time. (7)
  2. 3. Lets them dine to see if they paid attention. (8)
  3. 4. They can flog ice to Eskimos and it somehow makes sense. (5)
  4. 5. Plump? That girl? You should see her dad. (6)