The only definite no no is agave, it is still a sugar, so must be avoided. The only two sweeteners that are allowed are stevia and xylitol, this is because neither of them affect your blood sugar and score zero on a gi (glycemic index) rating.
For the very beginning of the diet I would cut out yoghurt and brown rice as well, and then re introduce one at a time to see how they affect you.
If you want a milk, try making almond milk, it really is very easy. You will need to buy a nut milk bag, or some muslin fabric, but that’s all.
Soak 1/2 cup raw almonds overnight
Drain and blend with 2 cups water
Strain through a nut milk bag or muslin (squeeze out all the milk)
And that’s it, you have a pint of milk.
You can use the pulp then for making crackers, if you want.
A good breakfast I was having when, I first started, is quinoa/millet with some coconut oil mixed through, and some nuts &/ seeds.
I now often have celery and nut butter or a fresh vegetable juice.
It is worth doing some kind of cleanse/detox as this kind of kick starts your body into healing mode, but ai don’t think it’s essential. If you cut down on your intake of food gradually, over 5-7 days, then do the cleanse, you will find the lack of food easier to cope with as you’ve shrunk your stomach. Also, try not to do too much while you are cleansing, as you will have less energy.