Birçok = Many OR A lot of... (Singular Form).
Biraz = A little bit of... (Singular Form).
BAZI = Some... (Plural Form).
Her gün = Every day. Bütün gün = All the day. Bütün günler = All days.
BÜTÜN ELMAYI yedim = I ate the whole apple completely.
BÜTÜN ELMALAR yedim = I ate all the apples.
I am not sure..
"kişi" is singular and "kişiler" is plural, so unlike in English. Though there is "many people" in the sentence, It turned into "kişi" because "Birçok kişiler ..." is incorrect for Turkish grammar. Already you say "birçok" that means more than one, you don't need to say the plural suffix "-ler/-lar" too.
"Birçok kişi her gün bir elma yer." - Many people eat an apple a day.
Birçok kişi bir elma her gün yer - Many people eat an apple every day.
You have changed the Turkish question & your emphasis is on "an apple every day is eaten.
Duo's Turkish question places the emphasis on "every day an apple is eaten."
I'm saying your answer is also correct as the meaning is clear.
Gün & elma - (nouns) You have switched the nouns around & your answer is clear.
Turkish word order - “Türkçe söz dizimi.”
Subject/time expression/place expression/object/verb.
This Turkish word order grammar guide applies in most cases.
Hilmi, what do you think about this site on words'order in Turkish?: https://en.wikipedia.org/wiki/Turkish_grammar#Word_order. It seams to me that it plays down the question of words' order.