Learn Turkish: Adam aniden kayıverdi ve direğe çarpayazdı. - The man suddenly slipped and almost hit the pole.

This uses the approximative compound verb structure you are currently learning. It is formed by taking the verb root çarp (hit/crash), adding the connecting vowel -a (based on a-undotted vowel harmony), and then adding -yazmak. The suffix -(y)Ayazmak indicates that an action came dangerously close to happening, but ultimately didn't. Finally, the past tense -dı is added, making çarpayazdı ("he almost hit").

What is the -ıver part doing in the verb kayıverdi?

This is another type of compound verb called the accelerative (-(y)ıvermek). It indicates that an action happened quickly, suddenly, or without warning. Here, it attaches to the root kay (to slip), forming kayıvermek. With the past tense -di, kayıverdi means "he suddenly slipped."

Since kayıverdi already means he slipped suddenly, isn't the word aniden (suddenly) redundant?

Technically yes, but this kind of redundancy is very common and natural in Turkish. Using an adverb like aniden alongside an -(y)ıvermek verb serves as an intensifier. It emphasizes just how unexpectedly the action occurred, making the storytelling more dramatic.

Why is the word for "pole" written as direğe instead of just direk?