Learn German: Die Freundschaft braucht die Freiheit.

Both of these nouns use predictable feminine suffixes! Nouns ending in -schaft (like die Freundschaft) and -heit (like die Freiheit) are always feminine.

Why does the German sentence use die twice, but the English translation doesn't say "The friendship needs the freedom"?

In German, abstract concepts and general ideas (like friendship, freedom, love, or life) almost always take a definite article. English drops the article for these broad concepts, but German keeps it, which is why we see die before both nouns here.

Is the second die (in die Freiheit) in the nominative or accusative case?

It is in the accusative case because it is the direct object of the verb brauchen (to need). For feminine nouns, the accusative article (die) looks exactly the same as the nominative article (die), so it doesn't appear to change.

How do the suffixes -schaft and -heit change the meaning of the root words?

They work a lot like English suffixes. Adding -schaft to the noun der Freund (friend) creates die Freundschaft (friendship). Adding -heit to the adjective frei (free) creates the abstract noun die Freiheit (freedom).