Learn Hardcore Turkish: Açık pencereler odaya ferahlık katıyor. - Open windows add a sense of spaciousness to the room.

In Turkish, adjectives normally come directly before the noun they modify, so açık pencereler literally means “open windows.” Saying pencereler açık is also grammatical, but it behaves like a complete sentence fragment meaning “the windows are open.” In that position pencereler is the subject and açık is a predicate adjective (you could even add a form of olmak, as in pencereler açık ~ “the windows are open”). To describe “open windows” as a noun phrase, you put the adjective first.

Why is odaya in the dative case with -ya? Could we use oda or odayı instead?

The verb katmak (“to add”) requires the thing receiving the addition to be in the dative case: “to add X to Y.” Here, ferahlık is being added to the room, so oda takes the dative -ya → odaya.

oda (nominative) would be unnatural, because you’re not simply mentioning “room” but indicating direction/target.
odayı (accusative) would make sense only if you used a different verb, for example ferahlatmak (“to freshen”), which takes a direct object: Açık pencereler odayı ferahlatıyor.

What exactly does ferahlık mean, and how is it formed?

ferah is an adjective meaning “airy,” “spacious,” or “refreshing.” The suffix -lık (or -lik, -lık, -luk depending on vowel harmony) turns adjectives into abstract nouns. So:

ferah → “airy/refreshing”
ferahlık → “airiness,” “freshness,” or “a sense of spaciousness.”

What is the function of katmak in this sentence? Why “to add” instead of “to give” or “to make”?

In Turkish, katmak (“to add”) is commonly used to express that something contributes a certain quality to something else. English also says “these features add value,” “that touch adds charm,” etc.
Here, Açık pencereler odaya ferahlık katıyor literally means “Open windows add freshness to the room.” Using vermek (“to give”) or yapmak (“to make”) would be awkward: you don’t “give” freshness in Turkish, you “add” it.

Why is the verb katıyor not katıyorlar even though pencereler is plural?

Turkish verbs in the third person plural can drop the plural marker -lar/-ler on the verb, because the subject noun already shows plurality. Both forms are correct:

Açık pencereler odaya ferahlık katıyor. (common, concise)
Açık pencereler odaya ferahlık katıyorlar. (emphatic on “they”)
In everyday usage, speakers often omit the -lar/-ler on the verb when the subject noun is clearly plural.

Could we rephrase the sentence using ferahlatmak? What’s the nuance between ferahlık katmak and ferahlatmak?

Yes. You can say: Açık pencereler odayı ferahlatıyor.

ferahlatmak means “to make something fresh/cool.”
ferahlık katmak focuses on “adding a sense of freshness/airiness.”
Nuance: ferahlatıyor is more direct—“the windows freshen the room.” ferahlık katıyor is a bit more descriptive/poetic—“they impart a sense of freshness.”

How do you pronounce ferahlık, and where is the stress?

In Turkish, the main word-accent almost always falls on the last syllable. So ferahlık is pronounced fe-rah-LIK (stress on -lık). Likewise:

açık → a-CIK (stress on -cık)
pencereler → pen-ce-re-LER (stress on final -ler)
odaya → o-da-YA (stress on -ya)
katıyor → ka-TI-yor (stress on -tı-)