1 cup of cubed papaya contains 8g of sugar; so if you ate just this amount and barely any other sugar (17g for rest of day) then you can handle it. If you ate one whole papaya, it’d contain 22g of sugar which is way too much for the diet.
Sesame seeds, oat groats I would not eat myself personally until phase 2 or later.
I have never seen buckwheat groats, but assume it is made from buckwheat. This should be OK as long as you rotate it with other foods in your diet such as quinoa, millet, red/black rice, etc. If it contains any other bad ingredients such as honey, etc, I would avoid it.