Learn Turkish: Biz ıspanağı çiğ yemezdik. - We didn't use to eat the spinach raw.

It uses the negative aorist past tense, which describes past habits ("didn't use to" or "wouldn't"). It breaks down as ye- (eat) + -mez (negative aorist suffix) + -di (past tense marker) + -k (we).

Could we just say yemedik instead of yemezdik in this sentence?

Yemedik is the simple past tense, meaning "we didn't eat" (a one-time completed event in the past). Yemezdik specifically emphasizes a past habit, meaning "we didn't use to eat" or "we wouldn't eat".

Why does ıspanak (spinach) change to ıspanağı here?

Because we are talking about "the" spinach in a general but definite sense as the direct object of the verb, it takes the accusative case suffix -ı. Adding this vowel causes the hard final k in ıspanak to soften into a ğ.

Is çiğ (raw) an adjective or an adverb in this sentence?

It acts as an adverb here, describing the condition of the spinach during the action of eating. In Turkish, adjectives like çiğ are frequently used as adverbs without needing any extra suffixes.