Learn Farsi: التیام این زخم دردآگین طول می‌کشد.

The suffix -âgin (and its shorter form -gin) attaches to a noun to create an adjective meaning "full of" or "affected by" that noun. Here, dard (pain) plus -âgin becomes dardâgin (full of pain, or agonizing). At your level, it is important to know this is a more literary or poetic suffix; in everyday speech, you are much more likely to hear the common alternative dardnâk.

Where do the hidden Ezafe connectors go in the phrase eltiyâm in zakhm dardâgin?

The phrase is pronounced eltiyâm-e in zakhm-e dardâgin. The first Ezafe links the noun eltiyâm (healing) to the specific thing being healed, in zakhm (this wound). The second Ezafe connects the noun zakhm to its descriptive adjective dardâgin. Note that the demonstrative adjective in (this) never takes an Ezafe to connect to its noun.

Literally, tul mikeshad involves the word for "length". How does this translate to "takes time"?

The compound verb tul keshidan combines tul (length or duration) with the verb keshidan (to pull or draw). Literally meaning "to pull length," it is the standard Farsi idiom for an action or process taking a long time. You will use this exact phrase whenever you want to say something "takes time" or "lasts a while" to finish.

Is the noun eltiyâm used for recovering from any kind of general illness?