Learn Turkish: Ben hiç ekşi zeytin yemezdim. - I never used to eat sour olives.

When we combine the aorist negative with the past tense to talk about past habits ('used to not do something'), the -z stays for all persons! So while 'I don't eat' is yemem, 'I didn't use to eat' becomes yemezdim. We attach the past suffix -di and the personal ending -m directly to the general negative form yemez.

Does hiç mean 'never' or 'ever'? Why is the verb also negative?

Hiç means 'never' when used with a negative verb, and 'ever' in questions. Turkish requires double negatives here, so you must use a negative verb (yemezdim) when using hiç in a statement. While English uses a single negative ('I never used to eat'), Turkish essentially says 'I never didn't use to eat.'

The English translation says 'olives', but zeytin isn't plural. Why not zeytinler?

When a noun is a general direct object referring to a category rather than specific items, Turkish keeps it singular and drops the plural suffix. Because you are talking about the general concept of eating sour olives, not specific olives on a plate, zeytin stays singular.

Could I say yemiyordum (I wasn't eating) instead of yemezdim here?

You could, and native speakers often use the past continuous (-yordu) for past habits. However, yemezdim (the aorist past negative) is the most exact way to express 'I never used to eat.' It strongly emphasizes a long-term habit, a general rule you had for yourself, or your nature in the past.