When should cooking, cuisine, and cookery be used?

I have never really understood when the words cooking, cuisine and cookery should be used, and to what level they are synonymous. For example, in each example below, which could you use and why (or why not)?

• Sicilian cuisine is based on seafood
• the local cuisine is just fine, but their wine is terrible
• my wife is much better than me at cooking pasta
• Greg is more skilled than me in cookery
• I am taking cooking classes after work

Solution 1:

They are not entirely interchangeable, but are used in an overlapping fashion by many.

I believe the more accurate uses would be as follows:

• cooking is the process of preparing food, particularly by the application of heat
• cookery is the group of methods and techniques, the art and science, particular to the process of cooking
• cuisine is the type and style of cooking and food particular to a location or culture