Learn Turkish: Dağa tırmanıyorduk, az kalsın çığ düşüyordu. - We were climbing the mountain, an avalanche almost occurred.

When using az kalsın to talk about something that almost happened but didn't, Turkish uses the past continuous tense (-(i)yordu). Even though an avalanche is a sudden event, this tense acts as a counterfactual here, meaning 'it was on the verge of happening.'

Why is the verb düşüyordu (was falling) used to mean an avalanche 'occurred'?

In Turkish, avalanches don't 'happen' or 'occur' (olmak). The standard set phrase for an avalanche happening is çığ düşmek (literally 'avalanche falling').

Why is it dağa with the dative case instead of the accusative dağı?

While you climb a mountain in English (using a direct object), the Turkish verb tırmanmak (to climb) always takes the dative case (-(y)a / -(y)e). Think of it as climbing to or up onto the mountain.

Both verbs end in -yordu. Do they serve the same grammatical function in this sentence?

No, they do two different jobs! Tırmanıyorduk is a standard past continuous action describing a literal background event ('we were climbing'). Düşüyordu, however, is triggered by az kalsın and doesn't mean it was actually falling; it solely expresses the averted action ('it almost fell').