This post is confusing, are you looking to incorporate a ketogenic diet or do you just want to fast or both? You don't have to fast to be in Ketosis. Keto is about what you eat (low carb, mod/lowish protein, high fat). Fasting is about not eating...
You will not lose muscle while fasting and strength training. Strength training actually has the opposite affect. It's imperative for muscle mass retention. As long as you get enough protein (when you eat), you'll be fine.
If you are looking into a ketogenic diet, performing Insanity workouts 6 days a week will be a problem. Low Carb + high intensity training (with high frequency) don't mix all that well.
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