If you're hungry all the time are you getting enough protein? It fills you up the most of all the macronutrients. You should aim for 20-30g at each meal. I would stick to 1700 calories rather than 1500 so that you don't end up bingeing, make sure you get 7-9 hours sleep and stay well hydrated. Add in lots of fruit and veg.
Fasting can work but it's not for everyone, maybe you could do 500 cals each on 3 meals a day, then 200 on snacks. I had a lot of success on 16:8 (eating between 12 noon and 8pm) but now I'm at maintenance I have re-introduced breakfast. I also strength train / do a lot of high intensity exercise, and am in my 40s so better I don't skip breakfast anymore as I need the fuel.
Consistency is key with weight loss.
I googled the best vegetarian protein sources and they are:
Tofu
Lentils
Beans
Peas
Edamame
Quinoa
Soy milk
Oats
Nuts
So you could go with for example:
Porridge/soy milk/berries for breakfast
Quinoa topped with roast veg for lunch
Tofu stir fry / lentil curry / bean chilli for dinner
If you eat some meat then have chicken as loads of protein in that per gram.