Who is the child Saint John has on the plate?
It is Christ…you can tell by looking at the nimbus.
Why Jesus depicted like that?
In the Byzantine tradition St. John is known as the Forerunner ( the one who comes before)…his job was to prepare for Christs coming…a prophet. In the Icon you show with Christ portrayed on a dish…seems to me as St John pointing to the coming of the Eucharist, our REAL food.
And in fact, there have been Eucharistic Miracles in the East where the Consecrated Species have turned into a Child.
St Peter Mohyla makes specific reference to such miracles in his “Sluzhebnyk” where he states: “Remember, Priest, that if after the Canon, as a result of someone in the Church expressing a doubt about the Most Holy Eucharist, you see that the Bread has become real Flesh and the Wine - real Blood or else that a Child has appeared on the Altar - then know that this is no longer the Eucharist, but a Miracle of God, an expression of His righteous anger and dismay at someone’s doubt or lack of respect before His Holy Mysteries. You are then to set aside this Miracle and cover it with the vestments. Every so often you are to examine it to see if the Miracle has changed back into the Holy Eucharist. If, at the time of Communion, the Miracle still persists, then you are to take other bread and wine and serve the Eucharistic Canon over them for the Communion of the Faithful . . .”