If you drop carbs really low, and then you eat more protein than fat - your body will convert protein to glucose (via gluconeogenesis) thereby preventing ketosis. So you'll be burning glucose for energy (not muscle, and not ketones) which defeats the whole point of a CKD.
As for HIIT, go ahead if you've got the energy - but it might be pretty tough...and it won't likely be much fun.
In terms of meals - try the boards at c-k-d.com for suggestions. One easy way to get a lot of fat with minimal protein is to mix a little bit of protein powder (preferably a blend including casein) with a tablespoon or two of oil (flax, hemp, olive, and extra virgin coconut oil are all good choices). Once you're in ketosis you can get away with taking in more protein and less fat - but in the first day or two of the cycle it's important to keep fat intake high and protein relatively low.