It's a world class kitchen and the chef said they had everything, so that's the answer.

If you want more of an explanation than that, keep in mind that the restaurant had been up and running for a while, serving any number of diners any number of dishes. Plus, everyone who was living on the island would need a variety of food to eat themselves.

Any theorizing about why he had the ingredients other than "it's a kitchen and they have ingredients for food so people can eat" is nonsense.

As to your second question, the answer is No. She found a way to play his game and get out according to dining rules, plus she gave him back something he had lost: the joy of cooking. He never wanted or intended to kill her, so he was happy to find a loophole to let her leave.