Learn Farsi: شاهین برای رهاسازی بال می‌زد. - The falcon was flapping its wings for the release.

Those phrases imply a transaction, compensation, or reciprocal duty (like giving something 'in return for' something else). The falcon flapping its wings is an action done with the purpose of getting released, not a trade. Therefore, the standard preposition of purpose برای is the natural choice.

How is the noun رهاسازی constructed?

It is a compound noun made of رها (free) and the suffix سازی (making). The suffix comes from the verb ساختن (to make/build). Together, it literally means 'free-making' or the act of releasing.

The English translation says 'its wings', but the Farsi just says بال. Why isn't it plural or possessive?

In Farsi, بال زدن (literally 'wing-hitting') is a compound verb that means 'to flap wings'. The noun part of a compound verb usually stays generic and singular. Adding a plural marker (بال‌ها) or a possessive ending (بال‌هایش) is unnecessary because the whole phrase functions as a single unified action.

The verb می‌زد translates to 'was flapping'. Doesn't this tense also mean 'used to flap'?

Yes. The past imperfect tense in Farsi (formed with می + past stem) can describe either an ongoing action in the past ('was flapping') or a habitual past action ('used to flap'). Context tells us this describes a specific, continuous struggle rather than a habit.