Usage of the word 'whole' is almost always in reference to all of A [something]. Meaning, all of ONE single item. 'All' is very open-ended and can refer to any number. It can be used to fit into the context of the statement, but it can not be directly swapped. With regard to your first example, you would be better off using 'this' (pronoun) instead of 'the' as it points out a specific watermelon. "I can eat this whole watermelon." meaning you already have a watermelon and you are making the statement that you CAN eat it. If you didn't have a watermelon and wanted to express this, you would say, "I can eat a whole watermelon." To reference only your ability to.

"I can eat the whole watermelon" or "I can eat the entire watermelon" would be correct, if you're saying that you can finish one watermelon. If you say, "I can eat all the watermelon" (or, more properly, I can eat all of the watermelon), you're saying not that you can eat one watermelon, but all of the watermelons that are present. I recommend using your first answer. However, I don't recommend eating an entire watermelon. ;)