If your carbs are low enough then the fat won't automatically cause you to store fat but you still need to watch your calories. Things like Atkins/LCHF naturally control your calorie intake because you go into ketosis and you lose much of your appetite.
Are you tracking your food? You won't lose weight if you eat too many calories, regardless of how healthy those calories are.
Not sure because the protein is also low here. Protein must be high always and you can even completely ditch carbs. While I was losing weight I followed the ketogenic diet and it worked wonders. The idea is to 'kill fat with fat'. By consuming fat rich foods like avocado, nuts, cheese and protein rich foods like egg white, you make your body feel full. Then there won't be any room for carbs which is the culprit for weight gain. Try this for a month with 20 mins of brisk walking and share your progress here