Learn Turkish: Adam yeni bir albüm için plak arıyordu. - The man was looking for a vinyl record for a new album.

The root is ara- (to search/look for). When we add the present continuous suffix -ıyor, the final -a on the root changes to -ı due to vowel narrowing, giving us arıyor (is looking for). Then we add the past tense suffix -du to make it past continuous, resulting in arıyordu (was looking for).

Why doesn't plak have an accusative suffix (like plağı) since it is the object being looked for?

Because he is looking for any vinyl record, not a specific one. In Turkish, when a direct object is general or indefinite, it does not take the accusative case ending. It stays in its bare dictionary form.

Why is the word order yeni bir albüm instead of bir yeni albüm?

In Turkish, when you have an adjective and the indefinite article bir, the word bir almost always goes directly before the noun, right after the adjective. It translates literally as 'new a album'.

Does the word için (for) require a special case ending on albüm?