Not exactly, accusative case always adds an "en" to the word "ein" only if the noun is masculine. How does it relate to "den"? "einen Apfel" is the accusative for "an apple", "den Apfel" is the accusative for "the apple".
The word "die Lehrer" is not feminine, it is plural: "the teachers", but "die Zeitung" is feminine and it stays the same in accusative as: "Ich lese die Zeitung", same applies for "das" as for example: "Ich esse das Brot".
There is a grid explaning the accusative cases at the bottom of lesson 2.
I hope this helps. Sorry if my English is not good (not my native language)
Apfel is masculine, and here it's the direct object of the verb haben.
So you need the accusative case, and einen is the masculine accusative form of the indefinite article.
ein would either be masculine nominative (e.g. for a subject: ein Apfel liegt auf dem Tisch) or neuter nominative/accusative (e.g. ich habe ein Pferd).
The correct form of the verb depends on the subject.
Have another look at the tips+notes for the unit "Accusative Case": https://www.duolingo.com/skill/de/Accusative-Case -- it has a conjugation table for the verb haben.
I recommend that you always review the tips+notes before starting a new unit.
The tips+notes are currently only available on the Duolingo website, not in any of the apps yet. So using the website is best for learning the language.
In German, haben is a normal transitive verb that takes a direct object in the accusative case: ich esse einen Apfel, ich sehe einen Apfel, ich habe einen Apfel “I am eating an apple, I see an apple, I have an apple” are all exactly parallel grammatically.
Even in English, “have” takes a direct object in the objective case; for example, a kidnapper might say, “Are you looking for your daughter? We have her!” (And not “we have she”.)