why not :ten chłopak nie je jeszcze kolacji
Because that would mean that he isn't eating dinner yet = he hasn't even started.
But he got his supper, and he's finished eating.
Czy można tutaj użyć "więcej" zamiast "już"?
Nie bardzo. That would be like "is not eating more dinner", not "anymore".
Why does the adverb juz follow the verb
He was eating, and eating... and now he's not eating anymore. That sounds the most natural to me, although "Chłopiec już nie je kolacji" would be fine as well.