"My brother doesn't like healthy food."
Translation:Мой брат не любит полезную еду.
"здоровая пища" is used more commonly and sounds better that "полезная еда"
I don't think so. For me, «пища» sounds way too formal, I don't think I'd use it in colloquial speech at all.
It is formal indeed, but "здоровая пища" is a set phrase, it reminds every Russian of the famous book "Книга о вкусной и здоровой пище" which was first published in the USSR in 1950s and has come out in lots of editions since then. Besides, any noun derived from a verb sounds a bit formal in Russian; therefore, no Russian would ever say, "мне нравится полезная едa"; instead, we would say something like "я люблю есть то, что полезно для здоровья". In an informal conversation (and in good literature too) the preference is always given to the verb over a related noun.
I believe it does.