Learn Turkish: Kayalığa doğru yürüyorduk, az kalsın düşüyordum. - We were walking towards the cliff, I almost fell.

This is the core of how Turkish handles averted actions. When you pair az kalsın (almost) with the past continuous -yordu, it means the action was on the verge of happening but didn't. While English uses the simple past ('almost fell'), Turkish expresses this as an interrupted process: 'I was falling (but stopped).'

Can I use neredeyse instead of az kalsın in this sentence?

Yes, they are perfectly interchangeable here. Both mean 'almost' or 'nearly'. Az kalsın is a fixed idiom literally meaning 'let little remain' (from az, little, and kalsın, let it remain), which gives the vivid sense of 'very little stood between me and falling.'

Does az kalsın have to be placed immediately before the verb?

Generally, yes. Adverbs of degree like az kalsın or neredeyse usually sit right before the verb they modify (düşüyordum) to strongly emphasize the near-miss. In this specific sentence, it forms a short second clause, so putting it right before the verb is the most natural word order.

Why does kayalık change to kayalığa before doğru?