Pane can be in generic or proper sense. In the first sentence
Non mangi pane dal tempo delle medie
is is used in generic sense (any kind of bread). In the second sentence
Soffocherai se mangi il pane in quel modo
it is used in proper sense (that particular piece of bread).
In the sentence Vedo che mangi di nuovo pane the part di nuovo is an adverb (locuzione avverbiale), not to be interpreted as a preposition followed by an adjective modifying pane. It's an inseparable entity which means nuovamente, ancora (in English it could be rendered as again).
Let's examine instead *Tu lo mangi il pane, vero?”. This is very colloquial, a bit more formal it should be *Tu mangi pane, vero?”
Actually the choice between no article and article is not clearcut. For instance, I would prefer
È solo che non voglio che Dylan mangi pane bianco
where the site adds the article. Both versions are acceptable, though.
To the contrary, mela is the particular fruit and mangi mela is not acceptable, because one eats that apple; consider that bread comes in various formats and in olden times it used to be baked in quite big forms.
On the other hand, we say succo di mela, not succo della mela, because the juice is made from several apples and a particular apple cannot be distinguished.