Learn Turkish: Heyelan yüzünden yol kapalıydı, az kalsın kaza yapıyorduk. - The road was closed because of the landslide, we almost had an accident.

In Turkish, averted past actions—things that almost happened but didn't—are expressed using the past continuous tense (-yordu). The idea is that the action was on the verge of happening before it was stopped. If you used the simple past (kaza yaptık), it would mean you actually had the accident!

What is the literal meaning of az kalsın?

It literally translates to "let a little remain." It functions as an idiom meaning "almost" or "narrowly," emphasizing that there was only a tiny margin of time or space left before the event happened.

Could I use için instead of yüzünden to mean "because of" the landslide?

You could, but yüzünden is much more natural here. Yüzünden is specifically used when a cause leads to a negative or undesirable outcome. Since a landslide causing a closed road is a negative event, yüzünden ("due to the fault of" / "on account of") is the best choice.

Why is "we had an accident" translated using the verb yapmak (to make/do)?

English uses "have" for many experiences, but Turkish relies on helper verbs. Kaza yapmak is the fixed active phrase for a person getting into an accident. If you just wanted to state the fact that "an accident happened" without focusing on who was involved, you would use olmak instead: Kaza oldu.