Learn Hardcore Turkish: Çayı da demleyiverdim; herkes sıcacık içsin. - I quickly brewed the tea too; let everyone drink it warm.

çayı is the definite direct object: the accusative suffix -ı marks that it’s a specific tea (the tea).
Without the accusative, çay demledim means I brewed (some) tea, not a particular one.
Vowel harmony picks -ı after the back, unrounded vowel in çay. The y you see is part of the stem; it’s not a buffer here.

What does da add in çayı da?

da/de is the additive enclitic meaning also/too/as well. Here it means: I went ahead and brewed the tea, too.
It attaches to the word it emphasizes, so çayı da emphasizes the tea as the added item.

Why is it da, not de, and how do I spell it?

Choose da after back vowels (a, ı, o, u) and de after front vowels (e, i, ö, ü). The last vowel in çayı is ı, so it’s da.
The additive da/de is written as a separate word: çayı da.
Don’t confuse it with the locative suffix -da/-de (in/at/on), which is attached to the word: çayda would mean in the tea. The additive is never written as ta/te in standard spelling.

What nuance does -iver- add in demleyiverdim?

-iver- (from the auxiliary verb vermek) adds a sense of quick, easy, or spur-of-the-moment action, often with a friendly, no-big-deal tone: I just quickly brewed it / I went ahead and brewed it.
It can imply doing something as a small favor or without fuss.

Can you break down demleyiverdim morphologically?

demle-y-iver-di-m
- demle-: brew (tea)
- -y-: buffer consonant because the stem ends with a vowel and the next morpheme starts with one
- -iver-: quick/just-like-that auxiliary
- -di-: simple past
- -m: 1st person singular (I)

Could I just say Çayı da demledim? What changes?

Yes. demledim is neutral: I brewed it.
demleyiverdim adds quickness/spontaneity and a casual, helpful vibe. Without -iver-, you lose that nuance.

Why is there a y in demleyiverdim?

It’s a buffer consonant to prevent two vowels from clashing when demle- meets -iver-. Turkish commonly inserts y in such situations.

What does -sin in içsin express?

-sin is the 3rd person singular optative/wish mood: let him/her/they (sg.) drink.
It expresses a desire or encouragement rather than a factual statement. Other common optative forms: içeyim (let me drink), içelim (let’s drink), içsinler (let them drink). For 2nd person, Turkish typically uses the imperative (iç! / için!) in modern usage.

Why is it herkes içsin and not herkes içsinler?

herkes (everyone) is grammatically singular in Turkish, so the verb is singular: içsin.
Using a plural verb with herkes is nonstandard (though it may occur colloquially). Stick with singular.

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

sıcacık is an affectionate/intensifying form of sıcak (hot/warm), roughly nice and hot/piping hot.
It’s formed with the diminutive-intensifier -cık, with a phonological adjustment: sıcak → sıcacık. Similar patterns: yumuşak → yumuşacık.
It often conveys warmth/comfort rather than just high temperature.

Is sıcacık an adjective or an adverb here?

It’s an adjective used adverbially to describe the manner of drinking: drink it while it’s nice and hot. Turkish often uses adjectives adverbially without extra marking.
You could also use it attributively: sıcacık çay (nice hot tea).

Could I use sımsıcak or çok sıcak instead of sıcacık?

sımsıcak is a strong intensifier (very hot, emphatic).
çok sıcak is neutral-literal (very hot).
sıcacık adds a cozy, pleasing nuance. All are correct; choose based on tone.

Why omit the object in the second clause (herkes sıcacık içsin)?

Turkish drops repeated, inferable elements. çayı is understood from the first clause, so repeating it would be redundant.
If you want to be explicit, you can say herkes çayı sıcacık içsin, but it’s not necessary.

What’s the role of the semicolon here?

It links two closely related independent clauses, much like English: I went ahead and brewed the tea; let everyone drink it nice and hot.
You could also write a comma, or make the purpose explicit with diye: Çayı da demleyiverdim, herkes sıcacık içsin diye (I brewed the tea so that everyone can drink it hot).

Can da/de work as a connector meaning something like “and (then)”?

Yes, clause-final da/de can serve as a light connector in speech/writing: Demleyiverdim de herkes sıcacık içsin ≈ I brewed it and (so) everyone can drink it hot.
In your sentence, da is additive with çayı; moving da changes the focus/structure.

Can I change the focus by moving da or other words?

Yes. da/de attaches to whatever you want to mark as “also”:
- Ben de çayı demleyiverdim: I, too, brewed the tea.
- Çayı da ben demleyiverdim: It was me who brewed the tea as well (object-focused, then subject).
Turkish word order is flexible; SOV is default, but moving elements changes emphasis.