Low Carb Program.

Butter, cream, yoghurt, lard are animal fats

Hi @Derry

Lots of animal fats listed there.

As for no 2, dietary fat is fuel. The body has ways to utilise fat, protein and carbs for energy. If eaten in excess so that the excess needs to be stored.
However, in order to store energy in the cells the body requires insulin, and insulin is produced primarily to deal with dietary carbohydrate.

So by keeping carbs low enough, there is little insulin floating about, which limits the amount of energy that is stored as fat.

Some people lose weight just by cutting carbs enough.
Some people don't. They often find that combining low carb with calorie restriction works for them. For a while.
Of course, they then risk slowing their metabolisms through calorie restriction, and halting weight loss unless they lower their calories further.

Personally, I would rather be fat with a higher metabolism, than slim with a slowed metabolism.

There can be very few adults - particularly in old age, who have not done low calorie diets, and they are proven beyond all doubt, to slow the metabolism - it is a measurable factor.
Weightloss is another difficulty - not all weightloss is a reduction in body fat. At the moment I am not losing weight, but I am changing shape, and growing stronger too. For me, that is good. My poor old body had such a hammering on the low fat diet to lower cholesterol month after month - and if high cholesterol was bad for it then it continued in that sate, as the low fat diet did not lower my cholesterol. The low carb one did.
There are so many myths about what is 'healthy' that very little can be regarded as a simple truth any more.