1) Once liver and muscle glycogen are thoroughly depleted, you won't be able to avoid experiencing rapid fatigue during anaerobic activities. Fat cannot be burned anaerobically, so any ATP will need to be generated either from the little glycogen you have or creatine phosphate stores (which will be depleted within seconds). Also, the presence of lactic acid directly inhibits fatty acid oxidation. Increased fat consumption does, however, increase IMT stores which are glycogen sparing at reasonable (say <80% VO2max) intensities, and that glycogen sparing effect may be the stimulus behind the initial "oh this is so great" phenomenon (my speculation). But ketogenic diets can't be sustained if you want optimal anaerobic performance.
2) Maybe, maybe not. If you eat offal and all parts of an animal then you may be generally okay, but is it optimal for long-term health to eat no/very few vegetables? Likely not.
3) This is really tough to succinctly answer (you might argue this whole website is devoted to this and similar questions), so I'm just gonna pass :)
I haven't heard a whole lot of evidence that VLC diets yield great strength gains; however, the positive changes in anabolic hormones with increased fat consumption (by replacing carbs in a higher carb diet) are well-documented.
All of that said, feel free to give it a try. I did, but found that after several weeks my anaerobic performance decreased substantially. Adding a PWO banana shake and a sweet potato or two a day brought everything right back to normal. VLC diets sound cool on the surface, but in reality you can't ignore the higher oxygen efficiency when processing carbs vs. fats nor the fact that fat can't be burned anaerobically.