Learn Turkish: Melankolik günlerinde geveze insanlardan kaçardı. - On his melancholic days, he would run away from talkative people.

The -i is the third-person possessive suffix, giving us the meaning "his melancholic days" (it could also be "her" or "their" depending on context). In Turkish, whenever you attach a spatial case suffix (like the locative -de) to a word ending in a third-person possessive suffix, you must use the buffer letter -n-. So it breaks down cleanly as gün-ler-i-n-de (day-s-his-[buffer]-on).

Why use kaçardı instead of the standard past tense kaçtı or past continuous kaçıyordu?

kaçardı combines the aorist suffix (-ar) with the past tense suffix (-dı) to describe a repeated past habit. It translates perfectly to "he would run away" or "he used to run away." If you used kaçtı, it would mean he ran away on one specific occasion. If you used kaçıyordu, it would emphasize that he was running away at a specific interrupted moment in the past.

Why is insanlar in the ablative case (insanlardan) here?

Because of the verb kaçmak. While in English we might simply "avoid people" (using a direct object), the Turkish verb kaçmak means "to escape," "to run away," or "to avoid," and it always requires the ablative case (-dan/-den). You are conceptually running away from someone or something.

This lesson is about the conjunction kâh ... kâh ... (sometimes ... sometimes ...). How could we apply it to a sentence like this?