Hello Marylin, Yes, the Mediterranean diet has been shown to be effective for weight loss. However, you dip need to consume the right amounts of food (calories) to lose weight as that varies depending on age, gender activity level etc. Here is a link to the Greek Nutrition Guidelines that includes servings https://www.olivetomato.com/eat-like-greek-greek-dietary-guidelines-a-better-choice/
On a ketogenic diet, your entire body switches its fuel supply to run mostly on fat, burning fat 24-7. When insulin levels become very low, fat burning can increase dramatically. It becomes easier to access your fat stores to burn them off. This is great if you’re trying to lose weight, but there are also other less obvious benefits, such as less hunger and a steady supply of energy. This may help keep you alert and focused.