They also told me that fasting is not helpful as it can cause liver to turn fat into glucose which produce ketones
I would have a read about the difference between nutritional ketosis and ketoacidosis.
The amount of information the average NHS person doesn't know about nutritional ketosis is amazing.
- they usually have a knee jerk reaction that ALL ketones are bad - which is nonsense.
Here is a link to explain
http://www.truehealthunlimited.com/blog/lowcarbapproach
LCHF diets are designed to produce ketones and those ketones are an aid to maintaining excellent blood glucose levels.
I can't speak about your personal level of ketones, or your kidney stones, but providing people have enough insulin (either injected or produced by their own bodies), and their blood glucose doesn't go too high, ketones are not a risk.
Oh, and that comment about fasting - that is exactly what fasting is intended to do! So it looks like those NHS staff don't have a clue about fasting either...