There is extensive evidence for the benefit of the Mediterranean style low carb diet, including cutting your risk of heart disease and diabetes. It has even been found to reduce risk the risk of breast cancer, compared with those on a low-fat diet. Consuming extra virgin olive oil (the fresh squeezed juice of olives) seems to be particularly beneficial when it comes to cancer, perhaps because it contains compounds such as polyphenols which are known to be anti-inflammatory.
I personally don’t count anymore as I want this to be as easy and sustainable as possible. I have had years of counting calories and points, and this is incredibly liberating. I just don’t eat any sugars, grains or high carb foods any more so I am incredibly low carb all the time. When I was starting out I counted, just to see where my carbs were coming from and it was an eye opener. And yes you are correct, to go into ketosis anywhere between 20-50g carbs/day. Find out what works for you.
It will take a while to trust and adjust to your new appetite. I personally found when I was low fat and on Weight Watchers, I was ravenous all day long, so to be told eat what you like was difficult to understand. By eating more healthy fats especially, will keep you fuller for longer. And depending on how long you have been dieting for, and how insulin resistant you are, will depend on how long it takes for you to adjust appetite and weight. The odd person gains weight when they start because they don’t listen to their body. Remember to eat until 80% full (it takes a while for your stomach to register you have eaten your meal) and only eat when hungry. Don’t snack if you don’t have to. Are you really hungry or thirsty (similar feelings).
Use fat as a lever. We’ve been taught to fear fat, but don’t! Both keto and low carb are high fat diets. Fat is our source of energy as well as satiety. The key to understand, though, is that fat is a lever on a low carb or keto diet. Carbs and protein stay constant, and fat is the one you increase or decrease (push the lever up or down) to gain or lose weight, respectively. So if your goal is weight loss, eat enough fat to be satisfied, but there’s no need to “get your fats in” once you’re satisfied.