Learn Hardcore Turkish: Yeni reklam afişinde markanın logo ve simgesi birlikte yer alıyor. - The brand’s logo and symbol appear together on the new advertising poster.

afişinde = afiş (poster) + -i (3rd-person possessive/definiteness marker) + -nde (locative case “in”).
So literally afiş-i-nde means “in the poster” (here “the new ad poster”).

Why do we need the -i before the locative -nde? I thought locative was just -de or -da.

In Turkish, when you attach a case ending (like locative -de/-da) to a definite noun, you normally add the 3rd-person possessive suffix -i first. It isn’t really a “possessor” here but marks definiteness (“the poster”) and allows you to say “in the poster” rather than “in a poster.”
Without it, afişte could be “in a poster” (indefinite).

What role does markanın play? Is that the genitive case?

Yes. markanın = marka (brand) + -nın (genitive case, harmonizing to -ın) = “of the brand.” It marks marka as the possessor in the genitive–possessive construction.

If markanın is the possessor, why is only simgesi marked with a possessive suffix and not logo?

In Turkish, when you list more than one possessed noun under the same possessor, you only put the possessive suffix on the last noun. So
• markanın logo ve simgesi
both logo and simge belong to marka, but you only see -si on simgesi.

What exactly does birlikte yer alıyor mean? It sounds like “takes place together.”

Literally yer almak means “to take place” or “to occupy a place.” It’s an idiom for “to appear,” “be featured,” or “be included.” Adding birlikte (“together”) gives birlikte yer alıyor = “they appear together.”

Could we have said bulunuyor instead of yer alıyor?

Yes, markanın logo ve simgesi yeni reklam afişinde birlikte bulunuyor would also mean “the brand’s logo and symbol are together in the new ad poster.”
However, yer almak is more formal and common in publishing/advertising contexts to say “to be featured” or “take their spots.”

Why is the adjective order Yeni reklam afişinde rather than Reklam afişi yeni?

Turkish adjectives (or adjective phrases like yeni reklam) always precede the noun they modify (afiş). So yeni reklam afişi = “new ad poster.” Then you attach locative: yeni reklam afişi-nde.

If the brand had multiple logos, how would you pluralize?

Pluralize the possessed nouns before the possessive suffix, but keep the same pattern:
markanın logoları ve simgeleri
(markas’s logolar-ı and simge-ler-i) = “the brand’s logos and symbols.”