Learn Farsi: قندیل‌های ناشی از فرسایش، قطره قطره در حال تشکیل شدن هستند. - The stalactites resulting from erosion are forming drop by drop.

Even though nâshi az translates to a phrase ('resulting from'), nâshi is an adjective. Just like any other adjective modifying a noun, it connects to qandil-hâ (stalactites) using the ezafe (-ye). It then takes the preposition az before the noun that causes the result.

Could we swap nâshi az for dar asar-e (as a result of) in this exact spot?

Not in the exact same spot. nâshi az acts as an adjective modifying the stalactites. dar asar-e is a prepositional phrase that modifies the whole action. To use it, you would restructure the sentence to something like: dar asar-e farsâyesh, qandil-hâ... (As a result of erosion, the stalactites...).

How does repeating the word qatre change its grammatical role?

Repeating a noun in Farsi is a common way to turn it into an adverb of manner. qatre means 'drop', but qatre qatre means 'drop by drop'. This reduplication shows how the action is happening, similar to kam kam (little by little).

Why use dar hâl-e tashkil shodan hastand instead of the continuous auxiliary dârand tashkil mishavand?

Both show an ongoing action, but dar hâl-e followed by an infinitive (tashkil shodan) strongly emphasizes the slow process or state of an action. It is also a bit more formal and literary than the colloquial + conjugated verb structure, fitting this scientific context perfectly.