Learn Hardcore Turkish: Ben misafirler için çay demliyorum.

In Turkish the subject pronoun is optional because the verb ending already tells you who the subject is. Here demliyorum ends in -yum, marking 1st person singular, so you can drop ben and still say Misafirler için çay demliyorum without changing the meaning.

How is the present‐continuous form demliyorum built from the verb demlemek?

Start with the infinitive stem demle-.
Because the stem ends in a vowel, you drop that vowel when adding -iyor (with buffer i): deml + iyor → demliyor.
Add the 1st person singular ending -um, which harmonizes to -yum after a vowel: demliyorum (“I am brewing”).

What does için mean, and why does it come after misafirler?

için is a postposition meaning for (indicating purpose or beneficiary). In Turkish postpositions follow the noun they modify, so misafirler için literally means for the guests.

Why isn’t çay marked with the accusative suffix -ı (i.e. çayı demliyorum)?

Turkish uses the accusative on definite/specific objects. However, çay demlemek is a common, somewhat idiomatic phrase that normally omits the suffix. If you wanted to stress that particular tea, you could say çayı demliyorum, but everyday speech usually leaves it as çay demliyorum.

Could I say Ben misafirler için çay yapıyorum instead? What’s the difference between demlemek and yapmak?

Yes, çay yapıyorum (“I’m making tea”) is perfectly natural colloquially.

demlemek = “to brew/steep tea” (focus on the infusion step)
yapmak = “to make/do” (more general; could include boiling, serving, etc.)

Can I change the word order to Çay demliyorum misafirler için or Misafirler için çay demliyorum?

Yes. Turkish is relatively flexible about word order. The default is Subject–Object–Verb (Ben misafirler için çay demliyorum), but you can front or delay misafirler için or çay to shift emphasis without altering the basic meaning.

What case is misafirler in? There’s no suffix like -e, -i, or -de.

It’s in the nominative plural. Because için is a postposition (not a case ending), the noun it follows stays in the nominative. So you don’t add any extra suffix to misafirler before için.

Could we drop misafirler için altogether and just say Çay demliyorum?

Yes, if the context makes it clear for whom you’re brewing tea, you can omit that phrase. Turkish frequently leaves out known or obvious information, so Çay demliyorum alone can suffice in many situations.