CARVING THE BASKET:
1. Lay a dampened dish towel on a counter or table and place melon on top to prevent it from rolling.
2. With a water-soluble marker, draw an outline of a basket onto melon, making sure the handle is at least 1 1/4 inches wide.
3. Using a large, sharp knife, carefully cut melon along marker line.
4. Remove excess rind and set aside. With a melon baller, scoop out all the watermelon flesh and place in a large glass or ceramic bowl; set aside.
5. With a vegetable peeler, even out scalloped edges of watermelon. Cover watermelon basket with clear plastic wrap and set aside.
MAKING THE FRUIT SALAD:
1. With a melon baller, scoop out flesh from cataloupes and honeydews.
2. In a large bowl, combine sugar, lime juice, lemon juice, orange liquer and lime peel. Stir well.
3. Add all melon balls, strawberries and grapes; toss to combine. Allow fruit to chill in refrigerator for 30 minutes.
4. Just before serving, transfer fruit salad to watermelon basket.